minimax estimation of linear and quadratic functionals on sparsity classes for the gaussian sequence model we obtain nonasymptotic minimax rates of estimation of the linear quadratic and the ell 2 norm functionals on classes of sparse vectors and construct optimal estimators that attain these rates the main object of interest is the class b 0 s of s sparse vectors theta theta 1 dots theta d for which we also provide completely adaptive estimators independent of s and of the noise variance sigma having logarithmically slower rates than the minimax ones furthermore we obtain the minimax rates on the ell q balls b q r theta in mathbb r d theta q le r where 0 q le2 and theta q sum i 1 d theta i q 1 q this analysis shows that there are in general three zones in the rates of convergence that we call the sparse zone the dense zone and the degenerate zone while a fourth zone appears for estimation of the quadratic functional we show that as opposed to estimation of theta the correct logarithmic terms in the optimal rates for the sparse zone scale as log d s 2 and not as log d s for the class b 0 s the rates of estimation of the linear functional and of the ell 2 norm have a simple elbow at s sqrt d boundary between the sparse and the dense zones and exhibit similar performances whereas the estimation of the quadratic functional q theta reveals more complex effects the minimax risk on b 0 s is infinite and the sparseness assumption needs to be combined with a bound on the ell 2 norm finally we apply our results on estimation of the ell 2 norm to the problem of testing against sparse alternatives in particular we obtain a nonasymptotic analog of the ingster donoho jin theory revealing some effects that were not captured by the previous asymptotic analysis

estimation of the false discovery proportion with unknown dependence summary large scale multiple testing with correlated test statistics arises frequently in much scientific research incorporating correlation information in approximating the false discovery proportion fdp has attracted increasing attention in recent years when the covariance matrix of test statistics is known fan and his colleagues provided an accurate approximation of the fdp under arbitrary dependence structure and some sparsity assumption however the covariance matrix is often unknown in many applications and such dependence information must be estimated before approximating the fdp the estimation accuracy can greatly affect the fdp approximation in the current paper we study theoretically the effect of unknown dependence on the testing procedure and establish a general framework such that the fdp can be well approximated the effects of unknown dependence on approximating the fdp are in the following two major aspects through estimating eigenvalues or eigenvectors and through estimating marginal variances to address the challenges in these two aspects we firstly develop general requirements on estimates of eigenvalues and eigenvectors for a good approximation of the fdp we then give conditions on the structures of covariance matrices that satisfy such requirements such dependence structures include banded or sparse covariance matrices and conditional sparse precision matrices within this framework we also consider a special example to illustrate our method where data are sampled from an approximate factor model which encompasses most practical situations we provide a good approximation of the fdp via exploiting this specific dependence structure the results are further generalized to the situation where the multivariate normality assumption is relaxed our results are demonstrated by simulation studies and some real data applications

robust adaptive rate optimal testing for the white noise hypothesis abstract a new test is proposed for the weak white noise null hypothesis the test is based on a new automatic selection of the order for a box pierce 1970 test statistic or the test statistic of hong 1996 the heteroskedasticity and autocorrelation consistent hac critical values from lee 2007 are used allowing for estimation of the error term the data driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o n 1 2 provided there are sufficiently many of such coefficients a simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative

phase transitions for high dimensional clustering and related problems consider a two class clustering problem where we observe x i ell i mu z i z i stackrel mathit i i d sim n 0 i p 1 leq i leq n the feature vector mu in r p is unknown but is presumably sparse the class labels ell i in 1 1 are also unknown and the main interest is to estimate them we are interested in the statistical limits in the two dimensional phase space calibrating the rarity and strengths of useful features we find the precise demarcation for the region of impossibility and region of possibility in the former useful features are too rare weak for successful clustering in the latter useful features are strong enough to allow successful clustering the results are extended to the case of colored noise using le cam s idea on comparison of experiments we also extend the study on statistical limits for clustering to that for signal recovery and that for global testing we compare the statistical limits for three problems and expose some interesting insight we propose classical pca and important features pca if pca for clustering for a threshold t 0 if pca clusters by applying classical pca to all columns of x with an l 2 norm larger than t we also propose two aggregation methods for any parameter in the region of possibility some of these methods yield successful clustering we discover a phase transition for if pca for any threshold t 0 let xi t be the first left singular vector of the post selection data matrix the phase space partitions into two different regions in one region there is a t such that cos xi t ell rightarrow 1 and if pca yields successful clustering in the other cos xi t ell leq c 0 0 our results require delicate analysis especially on post selection random matrix theory and on lower bound arguments

changepoint estimation another look at multiple testing problems summary we consider large scale multiple testing for data that have locally clustered signals with this structure we apply techniques from change point analysis and propose a boundary detection algorithm so that the clustering information can be utilised consequently the precision of the multiple testing procedure is substantially improved we study tests with independent as well as dependent p values monte carlo simulations suggest that the methods perform well with realistic sample sizes and show improved detection ability compared with competing methods our procedure is applied to a genome wide association dataset of blood lipids

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

tests for high dimensional covariance matrices we propose tests for sphericity and identity of high dimensional covariance matrices the tests are nonparametric without assuming a specific parametric distribution for the data they can accommodate situations where the data dimension is much larger than the sample size namely the large p small n situations we demonstrate by both theoretical and empirical studies that the tests have good properties for a wide range of dimensions and sample sizes we applied the proposed test on a microarray dataset on yorkshire gilts and tested for the covariance structure for the expression levels for sets of genes

to how many simultaneous hypothesis tests can normal student s t or bootstrap calibration be applied in the analysis of microarray data and in some other contemporary statistical problems it is not uncommon to apply hypothesis tests in a highly simultaneous way the number n say of tests used can be much larger than the sample sizes n to which the tests are applied yet we wish to calibrate the tests so that the overall level of the simultaneous test is accurate often the sampling distribution is quite different for each test so there may not be an opportunity to combine data across samples in this setting how large can n be as a function of n before level accuracy becomes poor here we answer this question in cases where the statistic under test is of student s t type we show that if either the normal or student t distribution is used for calibration then the level of the simultaneous test is accurate provided that log n increases at a strictly slower rate than n 1 3 as n diverges on the other hand if bootstrap methods are used for calibration then we may choose log n almost as large as

exact calculations for false discovery proportion with application to least favorable configurations in a context of multiple hypothesis testing we provide several new exact calculations related to the false discovery proportion fdp of step up and step down procedures for step up procedures we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable which leads to explicit computations of the c d f the s th moment and the mean of the fdp the latter corresponding to the false discovery rate fdr for step down procedures we derive what is to our knowledge the first explicit formula for the fdr valid for any alternative c d f of the p values we also derive explicit computations of the power for both step up and step down procedures these formulas are explicit in the sense that they only involve the parameters of the model and the c d f of the order statistics of i i d uniform variables the p values are assumed either independent or coming from an equicorrelated multivariate normal model and an additional mixture model for the true false hypotheses is used this new approach is used to investigate new results which are of interest in their own right related to least most favorable configurations for the fdr and the variance of the fdp

a high order accurate parallel solver for maxwell s equations on overlapping grids a scheme for the solution of the time dependent maxwell s equations on composite overlapping grids is described the method uses high order accurate approximations in space and time for maxwell s equations written as a second order vector wave equation high order accurate symmetric difference approximations to the generalized laplace operator are constructed for curvilinear component grids the modified equation approach is used to develop high order accurate approximations that use only three time levels and have the same time stepping restriction as the second order scheme discrete boundary conditions for perfect electrical conductors and for material interfaces are developed and analyzed the implementation is optimized for component grids that are cartesian resulting in a fast and efficient method the solver runs on parallel machines with each component grid distributed across one or more processors numerical results in two and three dimensions are presented for the fourth order accurate version of the method these results demonstrate the accuracy and efficiency of the approach

a note on methods of restoring consistency to the bootstrap summary we consider the property of consistency and its relevance for determining the performance of the bootstrap we analyse various parametric bootstrap approximations to the distributions of the hodges and stein estimators whose behaviour is typical of that of super efficient estimators employed in wavelet regression kernel density estimation and nonparametric curve fitting our results reveal not only some of the difficulties in selecting good modifications to the intuitive bootstrap but also that inconsistent bootstrap approximations may perform better than consistent versions even in large samples

on the benjamini hochberg method we investigate the properties of the benjamini hochberg method for multiple testing and of a variant of storey s generalization of it extending and complementing the asymptotic and exact results available in the literature results are obtained under two different sets of assumptions and include asymptotic and exact expressions and bounds for the proportion of rejections the proportion of incorrect rejections out of all rejections and two other proportions used to quantify the efficacy of the method

a significance test for the lasso in the sparse linear regression setting we consider testing the significance of the predictor variable that enters the current lasso model in the sequence of models visited along the lasso solution path we propose a simple test statistic based on lasso fitted values called the covariance test statistic and show that when the true model is linear this statistic has an exp 1 asymptotic distribution under the null hypothesis the null being that all truly active variables are contained in the current lasso model our proof of this result for the special case of the first predictor to enter the model i e testing for a single significant predictor variable against the global null requires only weak assumptions on the predictor matrix x on the other hand our proof for a general step in the lasso path places further technical assumptions on x and the generative model but still allows for the important high dimensional case p n and does not necessarily require that the current lasso model achieves perfect recovery of the truly active variables of course for testing the significance of an additional variable between two nested linear models one typically uses the chi squared test comparing the drop in residual sum of squares rss to a formula see text distribution but when this additional variable is not fixed and has been chosen adaptively or greedily this test is no longer appropriate adaptivity makes the drop in rss stochastically much larger than formula see text under the null hypothesis our analysis explicitly accounts for adaptivity as it must since the lasso builds an adaptive sequence of linear models as the tuning parameter decreases in this analysis shrinkage plays a key role though additional variables are chosen adaptively the coefficients of lasso active variables are shrunken due to the formula see text penalty therefore the test statistic which is based on lasso fitted values is in a sense balanced by these two opposing properties adaptivity and shrinkage and its null distribution is tractable and asymptotically exp 1

optimal rates of convergence for estimating the null density and proportion of nonnull effects in large scale multiple testing an important estimation problem that is closely related to large scale multiple testing is that of estimating the null density and the proportion of nonnull effects a few estimators have been introduced in the literature however several important problems including the evaluation of the minimax rate of convergence and the construction of rate optimal estimators remain open in this paper we consider optimal estimation of the null density and the proportion of nonnull effects both minimax lower and upper bounds are derived the lower bound is established by a two point testing argument where at the core is the novel construction of two least favorable marginal densities f 1 and f 2 the density f 1 is heavy tailed both in the spatial and frequency domains and f 2 is a perturbation of f 1 such that the characteristic functions associated with f 1 and f 2 match each other in low frequencies the minimax upper bound is obtained by constructing estimators which rely on the empirical characteristic function and fourier analysis the estimator is shown to be minimax rate optimal compared to existing methods in the literature the proposed procedure not only provides more precise estimates of the null density and the proportion of the nonnull effects but also yields more accurate results when used inside some multiple testing procedures which aim at controlling the false discovery rate fdr the procedure is easy to implement and numerical results are given

robust inference in nonlinear models with mixed identification strength abstract the paper studies inference in regression models composed of nonlinear functions with unknown transformation parameters and loading coefficients that measure the importance of each component in these models non identification and weak identification present in multiple parts of the parameter space resulting in mixed identification strength for different unknown parameters this paper proposes robust tests and confidence intervals for sub vectors and linear functions of the unknown parameters in particular the results cover applications where some nuisance parameters are non identified under the null davies 1977 1987 and some nuisance parameters are subject to a full range of identification strength to construct this robust inference procedure we develop a local limit theory that models mixed identification strength the asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence a sequential argument is used to peel the criterion function based on identification strength of the parameters

innovated higher criticism for detecting sparse signals in correlated noise higher criticism is a method for detecting signals that are both sparse and weak although first proposed in cases where the noise variables are independent higher criticism also has reasonable performance in settings where those variables are correlated in this paper we show that by exploiting the nature of the correlation performance can be improved by using a modified approach which exploits the potential advantages that correlation has to offer indeed it turns out that the case of independent noise is the most difficult of all from a statistical viewpoint and that more accurate signal detection for a given level of signal sparsity and strength can be obtained when correlation is present we characterize the advantages of correlation by showing how to incorporate them into the definition of an optimal detection boundary the boundary has particularly attractive properties when correlation decays at a polynomial rate or the correlation matrix is toeplitz

on red black sor smoothing in multigrid optimal relaxation parameters are obtained for red black gauss seidel relaxation in multigrid solvers of a family of elliptic equations the resulting relaxation schemes are found to retain very high efficiency over an appreciable range of coefficients of the elliptic differential operator yielding simple inexpensive and fully parallelizable smoothers in many situations where less cost effective block and alternating direction schemes are commonly used

accurate and efficient p value calculation via gaussian approximation a novel monte carlo method abstractit is of fundamental interest in statistics to test the significance of a set of covariates for example in genome wide association studies a joint null hypothesis of no genetic effect is tested for a set of multiple genetic variants the minimum p value method higher criticism and berk jones tests are particularly effective when the covariates with nonzero effects are sparse however the correlations among covariates and the nongaussian distribution of the response pose a great challenge toward the p value calculation of the three tests in practice permutation is commonly used to obtain accurate p values but it is computationally very intensive especially when we need to conduct a large amount of hypothesis testing in this paper we propose a gaussian approximation method based on a monte carlo scheme which is computationally more efficient than permutation while still achieving similar accuracy we derive nonasymptotic approximation error bounds that could vanish in the limit even if

valid post selection inference it is common practice in statistical data analysis to perform data driven variable selection and derive statistical inference from the resulting model such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori we propose to produce valid post selection inference by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals simultaneity is required for all linear functions that arise as coefficient estimates in all submodels by purchasing simultaneity insurance for all possible submodels the resulting post selection inference is rendered universally valid under all possible model selection procedures this inference is therefore generally conservative for particular selection procedures but it is always less conservative than full scheffe protection importantly it does not depend on the truth of the selected submodel and hence it produces valid inference even in wrong models we describe the structure of the simultaneous inference problem and give some asymptotic results

on three grid fourier analysis for multigrid in this paper we present three grid fourier analysis for multigrid methods due to the recursive structure of a multigrid iteration this analysis can be deduced from the well known two grid fourier analysis the coarse grid correction part of multigrid algorithms can be more accurately evaluated with the three grid analysis we apply the analysis to several scalar equations and discretizations with an emphasis on problems with a multigrid coarse grid correction difficulty like upwind discretizations of the convection diffusion equation the main focus lies on possible improvements by carefully chosen galerkin operators and or by an additional acceleration with restarted gmres gmres m numerical test calculations validate the theoretical predictions

optimal detection of heterogeneous and heteroscedastic mixtures the problem of detecting heterogeneous and heteroscedastic gaussian mixtures is considered the focus is on how the parameters of heterogeneity heteroscedasticity and proportion of non null component influence the difficulty of the problem we establish an explicit detection boundary which separates the detectable region where the likelihood ratio test is shown to reliably detect the presence of non null effect from the undetectable region where no method can do so in particular the results show that the detection boundary changes dramatically when the proportion of nonnull component shifts from the sparse regime to the dense regime furthermore it is shown that the higher criticism test which does not require the specific information of model parameters is optimally adaptive to the unknown degrees of heterogeneity and heteroscedasticity in both the sparse and dense cases

a composite grid solver for conjugate heat transfer in fluid structure systems we describe a numerical method for modeling temperature dependent fluid flow coupled to heat transfer in solids this approach to conjugate heat transfer can be used to compute transient and steady state solutions to a wide range of fluid solid systems in complex two and three dimensional geometry fluids are modeled with the temperature dependent incompressible navier stokes equations using the boussinesq approximation solids with heat transfer are modeled with the heat equation appropriate interface equations are applied to couple the solutions across different domains the computational region is divided into a number of sub domains corresponding to fluid domains and solid domains there may be multiple fluid domains and multiple solid domains each fluid or solid sub domain is discretized with an overlapping grid the entire region is associated with a composite grid which is the union of the overlapping grids for the sub domains a different physics solver fluid solver or solid solver is associated with each sub domain a higher level multi domain solver manages the entire solution process we propose and analyze some centered discrete approximations to the interface equations that have some desirable stability properties the coupled interface equations may be solved directly when using explicit time stepping methods in the sub domains resulting in a strongly coupled approach the stability of the interface treatment in this case is independent of the relative sizes of the material properties in the two domains with the time step only depending on the usual von neumann conditions for each sub domain for implicit time stepping methods we solve the interface equations in a weakly coupled fashion to avoid forming a coupled implicit system across all sub domains the convergence of this approach does depend on the relative sizes of the thermal conductivities and diffusivities we analyze different iteration strategies for solving these implicit equations including the use of mixed robin approximations at the interface numerical results are presented to illustrate the method the accuracy of the technique is verified using the method of analytic solutions and by computing the solution to some heat exchanger problems where the exact solution is known the technique is also applied to the modeling of an inertial confinement fusion hohlraum target and the flow of coolant past an hexagonal array of heated fuel rods the multi domain solver runs in parallel on distributed memory computers and some parallel results are provided

rate of convergence of attractors for singularly perturbed semilinear problems abstract we exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation we estimate the convergence of attractors in the hausdorff metric by rate of convergence of resolvent operators application to spatial homogenization and large diffusion except in a neighborhood of a point will be considered

detection of correlations we consider the hypothesis testing problem of deciding whether an observed high dimensional vector has independent normal components or alternatively if it has a small subset of correlated components the correlated components may have a certain combinatorial structure known to the statistician we establish upper and lower bounds for the worst case minimax risk in terms of the size of the correlated subset the level of correlation and the structure of the class of possibly correlated sets we show that some simple tests have near optimal performance in many cases while the generalized likelihood ratio test is suboptimal in some important cases

the little bootstrap and other methods for dimensionality selection in regression x fixed prediction error abstract when a regression problem contains many predictor variables it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables usually a regression equation based on a few variables will be more accurate and certainly simpler there are various methods for picking good subsets of variables and programs that do such procedures are part of every widely used statistical package the most common methods are based on stepwise addition or deletion of variables and on best subsets the latter refers to a search method that given the number of variables to be in the equation say five locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations all of these procedures generate a sequence of regression equations the first based on one variable the next based on two variables and so on each member of this sequence is called a submodel and the number of variables in the e

computational and statistical boundaries for submatrix localization in a large noisy matrix we study in this paper computational and statistical boundaries for submatrix localization given one observation of one or multiple nonoverlapping signal submatrix of magnitude lambda and size k m times k n embedded in a large noise matrix of size m times n the goal is to optimal identify the support of the signal submatrix computationally and statistically two transition thresholds for the signal to noise ratio lambda sigma are established in terms of m n k m and k n the first threshold sf snr c corresponds to the computational boundary we introduce a new linear time spectral algorithm that identifies the submatrix with high probability when the signal strength is above the threshold sf snr c below this threshold it is shown that no polynomial time algorithm can succeed in identifying the submatrix under the hidden clique hypothesis the second threshold sf snr s captures the statistical boundary below which no method can succeed in localization with probability going to one in the minimax sense the exhaustive search method successfully finds the submatrix above this threshold in marked contrast to submatrix detection and sparse pca the results show an interesting phenomenon that sf snr c is always significantly larger than sf snr s under the sub gaussian error model which implies an essential gap between statistical optimality and computational efficiency for submatrix localization

upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions the motivations to study the problem considered in this paper come from the theory of composite materials where the heat diffusion properties can change from one part of the domain to another mathematically this leads to a nonlinear second order parabolic equation for which the diffusion coefficient becomes large in a subdomain 0 the equation is supplemented by a nonlinear boundary condition on and an initial condition the authors determine the form of the limit problem the so called shadow system which involves an evolution equation for the averages of the density over 0 the main results include global in time existence of solutions and upper semicontinuity of the associated global attractors when the system approaches the shadow system

continuity of the attractors in a singular problem arising in composite materials abstract in this paper we consider the second order parabolic problem pe u t e p e x u x e x c x u e f u e in 0 1 u e n b x u e g u e for x 0 1 where the diffusion coefficient becomes large in a subset which is interior to the interval 0 1 as e 0 we prove the existence of invariant manifolds for pe and using the transversality of invariant manifolds of hyperbolic points obtained in v l carbone j g ruas filho transversality of stable and unstable manifolds for parabolic problems arising in composite materials j math anal appl 303 2005 220 241 we prove that equation pe and its limit problem are topologically equivalent on the attractors

adaptive testing on a regression function at a point we consider the problem of inference on a regression function at a point when the entire function satisfies a sign or shape restriction under the null we propose a test that achieves the optimal minimax rate adaptively over a range of holder classes up to a log logn term which we show to be necessary for adaptation we apply the results to adaptive one sided tests for the regression discontinuity parameter under a monotonicity restriction the value of a monotone regression function at the boundary and the proportion of true null hypotheses in a multiple testing problem

parabolic problems with nonlinear boundary conditions and critical nonlinearities we prove existence uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions we study these problems with initial data in l q omega w 1 w q omega 1 q infinity or measures and with critically growing non linearities

dimension reduction for hypothesis testing in worst case scenarios this paper considers a one among many detection problem where one has to discriminate between pure noise and one among l alternatives that are known up to an amplitude factor two issues linked to high dimensionality arise in this framework first the computational complexity associated to the generalized likelihood ratio glr with the constraint of sparsity one inflates linearly with l which can be an obstacle when multiple data sets have to be tested second standard procedures based on dictionary learning aimed at reducing the dimensionality may suffer from severe power losses for some alternatives thus suggesting a worst case scenario strategy in the case where the learned dictionary has k 1 column we show that the exact solution of the resulting detection problem which can be formulated as a minimax problem can be obtained by quadratic programming because it allows a better sampling of the diversity of the alternatives the case k 1 is expected to improve the detection performances over the case k 1 the worst case analysis of this case which is more involved leads us to propose two minimax learning algorithms numerical results show that these algorithms indeed allow to increase performances over the k 1 case and are in fact comparable to the glr using the full set of alternatives while being computationally simpler

optimal classification in sparse gaussian graphic model consider a two class classification problem where the number of features is much larger than the sample size the features are masked by gaussian noise with mean zero and covariance matrix sigma where the precision matrix omega sigma 1 is unknown but is presumably sparse the useful features also unknown are sparse and each contributes weakly i e rare and weak to the classification decision by obtaining a reasonably good estimate of omega we formulate the setting as a linear regression model we propose a two stage classification method where we first select features by the method of innovated thresholding it and then use the retained features and fisher s lda for classification in this approach a crucial problem is how to set the threshold of it we approach this problem by adapting the recent innovation of higher criticism thresholding hct we find that when useful features are rare and weak the limiting behavior of hct is essentially just as good as the limiting behavior of ideal threshold the threshold one would choose if the underlying distribution of the signals is known if only somewhat surprisingly when omega is sufficiently sparse its off diagonal coordinates usually do not have a major influence over the classification decision compared to recent work in the case where omega is the identity matrix proc natl acad sci usa 105 2008 14790 14795 philos trans r soc lond ser a math phys eng sci 367 2009 4449 4470 the current setting is much more general which needs a new approach and much more sophisticated analysis one key component of the analysis is the intimate relationship between hct and fisher s separation another key component is the tight large deviation bounds for empirical processes for data with unconventional correlation structures where graph theory on vertex coloring plays an important role

proportion of non zero normal means universal oracle equivalences and uniformly consistent estimators d0 we propose a general approach to construct the universal oracle equivalence of the proportion the construction is based on the underlying characteristic function the oracle equivalence reduces the problem of estimating the proportion to the problem of estimating the oracle which is relatively easier to handle in fact the oracle equivalence naturally yields a family of estimators for the proportion which are consistent under mild conditions uniformly across a wide class of parameters the approach compares favourably with recent works by meinshausen and rice and genovese and wasserman in particular the consistency is proved for an unprecedentedly broad class of situations the class is almost the largest that can be hoped for without further constraints on the model we also discuss various extensions of the approach report results on simulation experiments and make connections between the approach and several recent procedures in large scale multiple testing including the false discovery rate approach and the local false discovery rate approach

a spectrally accurate method for overlapping grid solution of incompressible navier stokes equations an overlapping mesh methodology that is spectrally accurate in space and up to third order accurate in time is developed for solution of unsteady incompressible flow equations in three dimensional domains the ability to decompose a global domain into separate but overlapping subdomains eases mesh generation procedures and increases flexibility of modeling flows with complex geometries the methodology employs implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally accurate spatial interpolation and high order accurate temporal extrapolation and requires few if any iterations yet maintains the global accuracy and stability of the underlying flow solver the overlapping mesh methodology is thoroughly validated using two dimensional and three dimensional benchmark problems in laminar and turbulent flows the spatial and temporal convergence is documented and is in agreement with the nominal order of accuracy of the solver the influence of long integration times as well as inflow outflow global boundary conditions on the performance of the overlapping grid solver is assessed in a turbulent benchmark of fully developed turbulent pipe flow the turbulent statistics with the overlapping grids is validated against published available experimental and other computation data scaling tests are presented that show near linear strong scaling even for moderately large processor counts a novel overlapping grid method for incompressible flow equations is developed the overlapping grid method is based on spectral element discretization the method maintains global spectral accuracy with polynomial refinement an explicit interface extrapolation scheme for temporal coupling is proposed the scheme allows for high order temporal accuracy with only a few iterations

simultaneous control of all false discovery proportions in large scale multiple hypothesis testing closed testing procedures are classically used for familywise error rate fwer control but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion fdp in all subsets of the hypotheses in this paper we investigate the special case of closed testing with simes local tests we construct a novel fast and exact shortcut which we use to investigate the power of this method when the number of hypotheses goes to infinity we show that if a minimal amount of signal is present the average power to detect false hypotheses at any desired fdp level does not vanish additionally we show that the confidence bounds for fdp are consistent estimators for the true fdp for every non vanishing subset for the case of a finite number of hypotheses we show connections between simes based closed testing and the procedure of benjamini and hochberg

the fast adaptive composite grid method fac algorithms for advanced computers fac is a fast systematic process for the numerical solution of partial differential equations on adapted grids this paper reports on numerical studies with fac in advancing computing environments including simulations with multiprocessor array architectures and actual tests on the hep we also analyze the parallel complexity of fac for general local grid applications

multigrid approach to overset grid communication the nonaligned multigrid method is introduced as an alternative to boundary point interpolation for communication in overset grid systems the nonaligned multigrid method treats the individual grids as levels in a multigrid solution procedure this technique was able to converge 69 faster than standard boundary point interpolation for mach 2 flow over a 5 deg ramp and 28 faster for a more complex reflected shock case for these test cases the largest increase in convergence rate came from applying the nonaligned multigrid method to the communication between overset grids further coarsening of the global grid was next in effectiveness and coarsening of local grids gave little improvement

detection of an anomalous cluster in a network we consider the problem of detecting whether or not in a given sensor network there is a cluster of sensors which exhibit an unusual behavior formally suppose we are given a set of nodes and attach a random variable to each node we observe a realization of this process and want to decide between the following two hypotheses under the null the variables are i i d standard normal under the alternative there is a cluster of variables that are i i d normal with positive mean and unit variance while the rest are i i d standard normal we also address surveillance settings where each sensor in the network collects information over time the resulting model is similar now with a time series attached to each node we again observe the process over time and want to decide between the null where all the variables are i i d standard normal and the alternative where there is an emerging cluster of i i d normal variables with positive mean and unit variance the growth models used to represent the emerging cluster are quite general and in particular include cellular automata used in modelling epidemics in both settings we consider classes of clusters that are quite general for which we obtain a lower bound on their respective minimax detection rate and show that some form of scan statistic by far the most popular method in practice achieves that same rate within a logarithmic factor our results are not limited to the normal location model but generalize to any one parameter exponential family when the anoma lous clusters are large enough

properties of higher criticism under strong dependence the problem of signal detection using sparse faint information is closely related to a variety of contemporary statistical problems including the control of false discovery rate and classification using very high dimensional data each problem can be solved by conducting a large number of simultaneous hypothesis tests the properties of which are readily accessed under the assumption of independence in this paper we address the case of dependent data in the context of higher criticism methods for signal detection short range dependence has no first order impact on performance but the situation changes dramatically under strong dependence there although higher criticism can continue to perform well it can be bettered using methods based on differences of signal values or on the maximum of the data the relatively inferior performance of higher criticism in such cases can be explained in terms of the fact that under strong dependence the higher criticism statistic behaves as though the data were partitioned into very large blocks with all but a single representative of each block being eliminated from the dataset

the generalized higher criticism for testing snp set effects in genetic association studies abstractit is of substantial interest to study the effects of genes genetic pathways and networks on the risk of complex diseases these genetic constructs each contain multiple snps which are often correlated and function jointly and might be large in number however only a sparse subset of snps in a genetic construct is generally associated with the disease of interest in this article we propose the generalized higher criticism ghc to test for the association between an snp set and a disease outcome the higher criticism is a test traditionally used in high dimensional signal detection settings when marginal test statistics are independent and the number of parameters is very large however these assumptions do not always hold in genetic association studies due to linkage disequilibrium among snps and the finite number of snps in an snp set in each genetic construct the proposed ghc overcomes the limitations of the higher criticism by allowing for arbitrary correlation structures among the s

bootstrapping lasso estimators in this article we consider bootstrapping the lasso estimator of the regression parameter in a multiple linear regression model it is known that the standard bootstrap method fails to be consistent here we propose a modified bootstrap method and show that it provides valid approximation to the distribution of the lasso estimator for all possible values of the unknown regression parameter vector including the case where some of the components are zero further we establish consistency of the modified bootstrap method for estimating the asymptotic bias and variance of the lasso estimator we also show that the residual bootstrap can be used to consistently estimate the distribution and variance of the adaptive lasso estimator using the former result we formulate a novel data based method for choosing the optimal penalizing parameter for the lasso using the modified bootstrap a numerical study is performed to investigate the finite sample performance of the modified bootstrap the methodology prop

minimax adaptive tests for the functional linear model we introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output the test statistics combine multiple testing ideas and random projections of the input data through functional principal component analysis interestingly the procedures are completely data driven and do not require any prior knowledge on the smoothness of the slope nor on the smoothness of the covariate functions the levels and powers against local alternatives are assessed in a nonasymptotic setting this allows us to prove that these procedures are minimax adaptive up to an unavoidable log log n multiplicative term to the unknown regularity of the slope as a side result the minimax separation distances of the slope are derived for a large range of regularity classes a numerical study illustrates these theoretical results

discovering the false discovery rate summary i describe the background for the paper controlling the false discovery rate a new and powerful approach to multiple comparisons by benjamini and hochberg that was published in the journal of the royal statistical society series b in 1995 i review the progress since made on the false discovery rate as well as the major conceptual developments that followed

adaptive confidence intervals for the test error in classification the estimated test error of a learned classifier is the most commonly reported measure of classifier performance however constructing a high quality point estimator of the test error has proved to be very difficult furthermore common interval estimators e g confidence intervals are based on the point estimator of the test error and thus inherit all the difficulties associated with the point estimation problem as a result these confidence intervals do not reliably deliver nominal coverage in contrast we directly construct the confidence interval by using smooth data dependent upper and lower bounds on the test error we prove that for linear classifiers the proposed confidence interval automatically adapts to the nonsmoothness of the test error is consistent under fixed and local alternatives and does not require that the bayes classifier be linear moreover the method provides nominal coverage on a suite of test problems using a range of classification algorithms and sample sizes this ar

parametric rate inference for one sided differentiable parameters suppose one has a collection of parameters indexed by a possibly infinite dimensional set given data generated from some distribution the objective is to estimate the maximal parameter in this

robustness and accuracy of methods for high dimensional data analysis based on student s t statistic summary student s t statistic is finding applications today that were never envisaged when it was introduced more than a century ago many of these applications rely on properties e g robustness against heavy tailed sampling distributions that were not explicitly considered until relatively recently we explore these features of the t statistic in the context of its application to very high dimensional problems including feature selection and ranking the simultaneous testing of many different hypotheses and sparse high dimensional signal detection robustness properties of the t ratio are highlighted and it is established that those properties are preserved under applications of the bootstrap in particular bootstrap methods correct for skewness and therefore lead to second order accuracy even in the extreme tails indeed it is shown that the bootstrap and also the more popular but less accurate t distribution and normal approximations are more effective in the tails than towards the middle of the distribution these properties motivate new methods e g bootstrap based techniques for signal detection that confine attention to the significant tail of a statistic

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

an adaptive resampling test for detecting the presence of significant predictors this article investigates marginal screening for detecting the presence of significant predictors in high dimensional regression screening large numbers of predictors is a challenging problem due to the nonstandard limiting behavior of post model selected estimators there is a common misconception that the oracle property for such estimators is a panacea but the oracle property only holds away from the null hypothesis of interest in marginal screening to address this difficulty we propose an adaptive resampling test art our approach provides an alternative to the popular yet conservative bonferroni method of controlling family wise error rates art is adaptive in the sense that thresholding is used to decide whether the centered percentile bootstrap applies and otherwise adapts to the nonstandard asymptotics in the tightest way possible the performance of the approach is evaluated using a simulation study and applied to gene expression data and hiv drug resistance data

numerical zoom for multiscale problems with an application to nuclear waste disposal we analyse here a computational technique and error estimates for the numerical solution of some problems with multiple scales when the small scale is confined to geometrically small regions such as jumps of coefficients on curves and surfaces or complex variations of coefficients in small regions where numerical zooms can be made the method is an adaptation of the hilbert subspace decomposition method studied by the second author in a different context so the method is restated with all known results combined with the layer decomposition of s delpino o pironneau asymptotic analysis and layer decomposition for the couplex exercise in alain bourgeat michel kern eds computational geosciences vol 8 no 2 kluwer academics publishers 2004 pp 149 162 the method is applied to the numerical assessment of a nuclear waste repository site

on combinatorial testing problems we study a class of hypothesis testing problems in which upon observing the realization of an n dimensional gaussian vector one has to decide whether the vector was drawn from a standard normal distribution or alternatively whether there is a subset of the components belonging to a certain given class of sets whose elements have been contaminated that is have a mean different from zero we establish some general conditions under which testing is possible and others under which testing is hopeless with a small risk the combinatorial and geometric structure of the class of sets is shown to play a crucial role the bounds are illustrated on various examples

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

covariate assisted ranking and screening for large scale two sample inference author s cai t tony sun wenguang wang weinan abstract two sample multiple testing has a wide range of applications the conventionalpractice first reduces the original observations to a vector of p values and then chooses a cutoffto adjust for multiplicity however this data reduction step could cause significant loss ofinformation and thus lead to suboptimal testing procedures we introduce a new framework fortwo sample multiple testing by incorporating a carefully constructed auxiliary variable in inferenceto improve the power a data driven multiple testing procedure is developed by employinga covariate assisted ranking and screening cars approach that optimally combines the informationfrom both the primary and the auxiliary variables the proposed cars procedureis shown to be asymptotically valid and optimal for false discovery rate control the procedureis implemented in the r package cars numerical results confirm the effectiveness of carsin false discovery rate control and show that it achieves substantial power gain over existingmethods cars is also illustrated through an application to the analysis of a satellite imagingdata set for supernova detection

estimation and confidence sets for sparse normal mixtures for high dimensional statistical models researchers have begun to focus on situations which can be described as having relatively few moderately large coefficients such situations lead to some very subtle statistical problems in particular ingster and donoho and jin have considered a sparse normal means testing problem in which they described the precise demarcation or detection boundary meinshausen and rice have shown that it is even possible to estimate consistently the fraction of nonzero coordinates on a subset of the detectable region but leave unanswered the question of exactly in which parts of the detectable region consistent estimation is possible in the present paper we develop a new approach for estimating the fraction of nonzero means for problems where the nonzero means are moderately large we show that the detection region described by ingster and donoho and jin turns out to be the region where it is possible to consistently estimate the expected fraction of nonzero coordinates this theory is developed further and minimax rates of convergence are derived a procedure is constructed which attains the optimal rate of convergence in this setting furthermore the procedure also provides an honest lower bound for confidence intervals while minimizing the expected length of such an interval simulations are used to enable comparison with the work of meinshausen and rice where a procedure is given but where rates of convergence have not been discussed extensions to more general gaussian mixture models are also given

revisiting multi subject random effects in fmri advocating prevalence estimation abstract random effect analysis has been introduced into fmri research in order to generalize findings from the study group to the whole population generalizing findings is obviously harder than detecting activation within the study group since in order to be significant an activation has to be larger than the inter subject variability indeed detected regions are smaller when using random effect analysis versus fixed effects the statistical assumptions behind the classic random effect model are that the effect in each location is normally distributed over subjects and activation refers to a non null mean effect we argue that this model is unrealistic compared to the true population variability where due to function anatomy inconsistencies and registration anomalies some of the subjects are active and some are not at each brain location we propose a gaussian mixture random effect that amortizes between subject spatial disagreement and quantifies it using the prevalence of activation at each location we present a formal definition and an estimation procedure of this prevalence the end result of the proposed analysis is a map of the prevalence at locations with significant activation highlighting activation regions that are common over many brains prevalence estimation has several desirable properties a it is more informative than the typical active inactive paradigm b in contrast to the usual display of p values in activated regions which trivially converge to 0 for large sample sizes prevalence estimates converge to the true prevalence

higher criticism for detecting sparse heterogeneous mixtures higher criticism or second level significance testing is a multiplecomparisons concept mentioned in passing by tukey it concerns a situation where there are many independent tests of significance and one is interested in rejecting the joint null hypothesis tukey suggested comparing the fraction of observed significances at a given level to the expected fraction under the joint null in fact he suggested standardizing the difference of the two quantities and forming a z score the resulting z score tests the significance of the body of significance tests we consider a generalization where we maximize this z score over a range of significance levels 0 0 we are able to show that the resulting higher criticism statistic is effective at resolving a very subtle testing problem testing whether n normal means are all zero versus the alternative that a small fraction is nonzero the subtlety of this sparse normal means testing problem can be seen from work of ingster and jin who studied such problems in great detail in their studies they identified an interesting range of cases where the small fraction of nonzero means is so small that the alternative hypothesis exhibits little noticeable effect on the distribution of the p values either for the bulk of the tests or for the few most highly significant tests in this range when the amplitude of nonzero means is calibrated with the fraction of nonzero means the likelihood ratio test for a precisely specified alternative would still succeed in separating the two hypotheses we show that the higher criticism is successful throughout the same region of amplitude sparsity where the likelihood ratio test

statistical inference of genetic pathway analysis in high dimensions genetic pathway analysis has become an important tool for investigating the association between a group of genetic variants and traits with dense genotyping and extensive imputation the number of genetic variants in biological pathways has increased considerably and sometimes exceeds the sample size formula see text conducting genetic pathway analysis and statistical inference in such settings is challenging we introduce an approach that can handle pathways whose dimension formula see text could be greater than formula see text our method can be used to detect pathways that have nonsparse weak signals as well as pathways that have sparse but stronger signals we establish the asymptotic distribution for the proposed statistic and conduct theoretical analysis on its power simulation studies show that our test has correct type i error control and is more powerful than existing approaches an application to a genome wide association study of high density lipoproteins demonstrates the proposed approach

fast generalized subset scan for anomalous pattern detection we propose fast generalized subset scan fgss a new method for detecting anomalous patterns in general categorical data sets we frame the pattern detection problem as a search over subsets of data records and attributes maximizing a nonparametric scan statistic over all such subsets we prove that the nonparametric scan statistics possess a novel property that allows for efficient optimization over the exponentially many subsets of the data without an exhaustive search enabling fgss to scale to massive and high dimensional data sets we evaluate the performance of fgss in three real world application domains customs monitoring disease surveillance and network intrusion detection and demonstrate that fgss can successfully detect and characterize relevant patterns in each domain as compared to three other recently proposed detection algorithms fgss substantially decreased run time and improved detection power for massive multivariate data sets

distributions and power of optimal signal detection statistics in finite case for detecting weak and sparse signals by a set of n input p values the higher criticism hc type statistics the berk jones b j type statistics and the phi divergence statistics have the equivalent asymptotic optimality as n goes to infinity however they can have significantly different performance in practical data analysis where n is always finite and even very small to address this problem in a broader context this paper introduces a general family of goodness of fit statistics called the ggof which unifies a broad signal detection statistics including these optimal ones efficient and accurate analytical calculations for the distributions of the ggof statistics are provided under arbitrary i i d continuous models of the null and the alternative hypotheses based on that a systematic power study reveals that in finite case the number of signals is often more relevant than the signal proportion the hc and the reverse hc have advantages for relatively sparser and denser signals respectively while the b j is more robust a general framework is given to apply the ggof into data analysis based on the generalized linear models an application to the snp set based genome wide association study gwas for crohn s disease shows that these optimal statistics have a good potential for detecting novel disease genes with weak snp effects the calculations have been implemented into an r package settest and published on the cran

direct numerical simulation of particulate flows with an overset grid method abstract we evaluate an efficient overset grid method for two dimensional and three dimensional particulate flows for small numbers of particles at finite reynolds number the rigid particles are discretised using moving overset grids overlaid on a cartesian background grid this allows for strongly enforced boundary conditions and local grid refinement at particle surfaces thereby accurately capturing the viscous boundary layer at modest computational cost the incompressible navier stokes equations are solved with a fractional step scheme which is second order accurate in space and time while the fluid solid coupling is achieved with a partitioned approach including multiple sub iterations to increase stability for light rigid bodies through a series of benchmark studies we demonstrate the accuracy and efficiency of this approach compared to other boundary conformal and static grid methods in the literature in particular we find that fully resolving boundary layers at particle surfaces is crucial to obtain accurate solutions to many common test cases with our approach we are able to compute accurate solutions using as little as one third the number of grid points as uniform grid computations in the literature a detailed convergence study shows a 13 fold decrease in cpu time over a uniform grid test case whilst maintaining comparable solution accuracy

testing for marginal linear effects in quantile regression this paper develops a new marginal testing procedure to detect the presence of significant predictors associated with the conditional quantiles of a scalar response the idea is to fit the marginal quantile regression on each predictor one at a time and then base the test on the t statistics associated with the most predictive predictors a resampling method is devised to calibrate this test statistic which has non regular limiting behavior due to the selection of the most predictive variables asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified even though a fixed dimension is assumed to derive the asymptotic results the proposed test is applicable and computationally feasible for large dimensional predictors the method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response the approach is illustrated using an application to an hiv drug resistance dataset

optimal detection of sparse mixtures against a given null distribution detection of sparse signals arises in a wide range of modern scientific studies the focus so far has been mainly on gaussian mixture models in this paper we consider the detection problem under a general sparse mixture model and obtain explicit expressions for the detection boundary under mild regularity conditions in addition for gaussian null hypothesis we establish the adaptive optimality of the higher criticism procedure for all sparse mixtures satisfying the same conditions in particular the general results obtained in this paper recover and extend in a unified manner the previously known results on sparse detection far beyond the conventional gaussian model and other exponential families

can one estimate the conditional distribution of post model selection estimators we consider the problem of estimating the conditional distribution of a post model selection estimator where the conditioning is on the selected model the notion of a post model selection estimator here refers to the combined procedure resulting from first selecting a model e g by a model selection criterion such as aic or by a hypothesis testing procedure and then estimating the parameters in the selected model e g by least squares or maximum likelihood all based on the same data set we show that it is impossible to estimate this distribution with reasonable accuracy even asymptotically in particular we show that no estimator for this distribution can be uniformly consistent not even locally this follows as a corollary to local minimax lower bounds on the performance of estimators for this distribution similar impossibility results are also obtained for the conditional distribution of linear functions e g predictors of the post model selection estimator

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

estimation of a two component mixture model with applications to multiple testing we consider a two component mixture model with one known component we develop methods for estimating the mixing proportion and the other unknown distribution nonparametrically given i i d data from the mixture model we use ideas from shape restricted function estimation and develop tuning parameter free estimators that are easily implementable and have good finite sample performance we establish the consistency of our procedures distribution free finite sample lower confidence bounds are developed for the mixing proportion the identifiability of the model and the estimation of the density of the unknown mixing distribution are also addressed we discuss the connection with the problem of multiple testing and compare our procedure with some of the existing methods in that area through simulation studies we also analyse two data sets one arising from an application in astronomy and the other from a microarray experiment

a morse smale ordinary differential equation in rn abstract in this paper we develop some results on morse smale parabolic differential equation we prove that the limiting problem of morse smale parabolic equations is also morse smale the assumptions for obtaining this result are compact convergence of resolvent operators and the gap condition on eigenvalues as application we exhibit a morse smale ordinary differential equation in r n for each n 2 and a scalar morse smale semilinear equation with localized large diffusion

testing for the presence of significant covariates through conditional marginal regression summary researchers sometimes have a priori information on the relative importance of predictors that can be used to screen out covariates an important question is whether any of the discarded covariates have predictive power when the most relevant predictors are included in the model we consider testing whether any discarded covariate is significant conditional on some pre chosen covariates we propose a maximum type test statistic and show that it has a nonstandard asymptotic distribution giving rise to the conditional adaptive resampling test to accommodate signals of unknown sparsity we develop a hybrid test statistic which is a weighted average of maximum and sum type statistics we prove the consistency of the test procedure under general assumptions and illustrate how it can be used as a stopping rule in forward regression we show through simulation that the proposed method provides adequate control of the familywise error rate with competitive power for both sparse and dense signals even in high dimensional cases and we demonstrate its advantages in cases where the covariates are heavily correlated we illustrate the application of our method by analysing an expression quantitative trait locus dataset

cauchy combination test a powerful test with analytic p value calculation under arbitrary dependency structures abstract combining individual p values to aggregate multiple small effects has a long standing interest in statistics dating back to the classic fisher s combination test in modern large scale da

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments

on multigrid for overlapping grids the solution of elliptic partial differential equations on composite overlapping grids using multigrid is discussed an approach is described that provides a fast and memory efficient scheme for the solution of boundary value problems in complex geometries the key aspects of the new scheme are an automatic coarse grid generation algorithm an adaptive smoothing technique for adjusting residuals on different component grids and the use of local smoothing near interpolation boundaries other important features include optimizations for cartesian component grids the use of over relaxed red black smoothers and the generation of coarse grid operators through galerkin averaging numerical results in two and three dimensions show that very good multigrid convergence rates can be obtained for dirichlet neumann and mixed boundary conditions a comparison to krylov based solvers shows that the multigrid solver can be much faster and require significantly less memory

semilinear high dimensional model for normalization of microarray data a theoretical analysis and partial consistency normalization of microarray data is essential for removing experimental biases and revealing meaningful biological results motivated by a problem of normalizing microarray data a semilinear in slide model slim has been proposed to aggregate information from other arrays slim is generalized to account for across array information resulting in an even more dynamic semiparametric regression model this model can be used to normalize microarray data even when there is no replication within an array we demonstrate that this semiparametric model has a number of interesting features the parametric component and the nonparametric component that are of primary interest can be consistently estimated the former having a parametric rate and the latter having a nonparametric rate whereas the nuisance parameters cannot be consistently estimated this is an interesting extension of the partial consistent phenomena which itself is of theoretical interest the asymptotic normality for the parametric component

calculation of flows using three dimensional overlapping grids and multigrid methods a computational methodology combining overlapping grid techniques with multigrid methods has been developed for three dimensional flow calculations in or around complex geometries the computational accuracy efficiency and capability of the present approach are investigated in this paper the incompressible navier stokes equations are discretized using a finite volume method on a semi staggered grid the discrete problem is solved by a multigrid algorithm some numerical examples are chosen for evaluating numerical accuracy a a straight pipe for which the exact solution is known b curved pipes where previous experimental and numerical data are available c an axisymmetric sudden expansion the performance of the multigrid method on overlapping grids is assessed several cases of flows in stationary and time dependent complex geometries are given to demonstrate the capability and the potential of the methods that we employ