ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

point estimation with exponentially tilted empirical likelihood parameters defined via general estimating equations gee can be estimated by maximizing the empirical likelihood el newey and smith econometrica 72 2004 219 255 have recently shown that this el estimator exhibits desirable higher order asymptotic properties namely that its o n 1 bias is small and that bias corrected el is higher order efficient although el possesses these properties when the model is correctly specified this paper shows that in the presence of model misspecification el may cease to be root n convergent when the functions defining the moment conditions are unbounded even when their expectations are bounded in contrast the related exponential tilting et estimator avoids this problem this paper shows that the et and el estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood etel exhibiting the same o n 1 bias and the same o n 2 variance as el while maintaining root n convergence under model misspecification

post fisherian experimentation from physical to virtual fisher s pioneering work in design of experiments has inspired further work with broader applications especially in industrial experimentation this article discusses three topics in physical experiments principles of effect hierarchy sparsity and heredity for factorial designs a new method called conditional main effect cme for de aliasing aliased effects and robust parameter design i also review the recent emergence of virtual experiments on a computer some major challenges in computer experiments which must go beyond fisherian principles are outlined

efficient empirical bayes variable selection and estimation in linear models we propose an empirical bayes method for variable selection and coefficient estimation in linear regression models the method is based on a particular hierarchical bayes formulation and the empirical bayes estimator is shown to be closely related to the lasso estimator such a connection allows us to take advantage of the recently developed quick lasso algorithm to compute the empirical bayes estimate and provides a new way to select the tuning parameter in the lasso method unlike previous empirical bayes variable selection methods which in most practical situations can be implemented only through a greedy stepwise algorithm our method gives a global solution efficiently simulations and real examples show that the proposed method is very competitive in terms of variable selection estimation accuracy and computation speed compared with other variable selection and estimation methods

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

heuristics of instability and stabilization in model selection in model selection usually a best predictor is chosen from a collection hat mu cdot s of predictors where hat mu cdot s is the minimum least squares predictor in a collection mathsf u s of predictors here s is a complexity parameter that is the smaller s the lower dimensional smoother the models in mathsf u s if mathsf l is the data used to derive the sequence hat mu cdot s the procedure is called unstable if a small change in mathsf l can cause large changes in hat mu cdot s with a crystal ball one could pick the predictor in hat mu cdot s having minimum prediction error without prescience one uses test sets cross validation and so forth the difference in prediction error between the crystal ball selection and the statistician s choice we call predictive loss for an unstable procedure the predictive loss is large this is shown by some analytics in a simple case and by simulation results in a more complex comparison of four different linear regression methods unstable procedures can be stabilized by perturbing the data getting a new predictor sequence hat mu cdot s and then averaging over many such predictor sequences

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

a bayesian variable selection approach for analyzing designed experiments with complex aliasing experiments using designs with complex aliasing patterns are often performed for example twolevel nongeometric plackett burman designs multilevel and mixed level fractional factorial designs two level fractional factorial designs with hard to control factors and supersaturated designs hamada and wu proposed an iterative guided stepwise regression strategy for analyzing the data from such designs that allows entertainment of interactions their strategy provides a restricted search in a rather large model space however this article provides an efficient methodology based on a bayesian variable selection algorithm for searching the model space more thoroughly we show how the use of hierarchical priors provides a flexible and powerful way to focus the search on a reasonable class of models the proposed methodology is demonstrated with four examples three of which come from actual industrial experiments

a high order isoparametric finite element method for the computation of waveguide modes we have studied the approximation of optical waveguide eigenvalues by a high order isoparametric vector finite element method isoparametric mappings are used for the approximation of domains with curved boundaries or curved material interfaces eigenvalue convergence for curved elements is investigated numerical results verify the predicted order of convergence and show the remarkable accuracy of the method

high order matched interface and boundary methods for the helmholtz equation in media with arbitrarily curved interfaces this work overcomes the difficulty of the previous matched interface and boundary mib method in dealing with interfaces with non constant curvatures for optical waveguide analysis this difficulty is essentially bypassed by avoiding the use of local cylindrical coordinates in the improved mib method instead novel jump conditions are derived along global cartesian directions for the transverse magnetic field components effective interface treatments are proposed to rigorously impose jump conditions across arbitrarily curved interfaces based on a simple cartesian grid even though each field component satisfies the scalar helmholtz equation the enforcement of jump conditions couples two transverse magnetic field components so that the resulting mib method is a full vectorial approach for the modal analysis of optical waveguides the numerical performance of the proposed mib method is investigated by considering interface problems with both constant and general curvatures the mib method is shown to be able to deliver a fourth order of accuracy in all cases even when a high frequency solution is involved

a second order dispersive fdtd algorithm for transverse electric maxwell s equations with complex interfaces this work overcomes the difficulty of the finite difference time domain fdtd algorithm in solving the transverse electric te maxwell s equations with inhomogeneous dispersive media for such te problems the electric fields are discontinuous across the dispersive interfaces moreover such discontinuities are time variant a novel matched interface and boundary time domain mibtd method is proposed to solve such problems through new developments in both mathematical formulations and numerical algorithms mathematically instead of handling all zeroth and first order jump conditions in a local coordinate we directly construct the te jump conditions which are needed in the fdtd computations in the cartesian coordinate such cartesian direction conditions depend on the time as well as tangential and normal components of the electric flux driven by the jump condition modeling we adopt the standard maxwell s equations in coupling with the debye auxiliary differential equations for the electric flux as the governing equations computationally the leapfrog scheme is employed for integrating the maxwell system and time dependent jump conditions sophisticated interface treatments are developed in both producing the te jump conditions and enforcing them in the fdtd algorithm based on a staggered yee lattice the numerical accuracy stability and efficiency of the proposed scheme are investigated by considering dispersive interfaces of various shapes the mibtd method achieves a spatially second order of convergence in all tests to the best of our knowledge the present mibtd scheme is the first fdtd method in the literature that can restore second order accuracy in treating curved dispersive interfaces for the te maxwell system

approximations to the profile empirical likelihood function for a scalar parameter in the context of m estimation summary empirical likelihood possesses many of the important properties of genuine parametric likelihood but it is computationally burdensome especially when nuisance parameters are present this paper presents two approximations to the profile empirical likelihood function for a scalar parameter of interest in the context of m estimation the simpler approximation is based on the third derivative of the profile log empirical likelihood function at its maximising point while the more accurate approximation involves both the third and fourth derivatives formulae are given for these higher order derivatives that can be evaluated using ordinary matrix operations so computation of the approximations is very easy the accuracy of the approximations is demonstrated in several numerical examples the computational simplicity of the approximations makes it feasible to use them in conjunction with bootstrap calibration for constructing accurate confidence intervals and limits the derivatives are also helpful for exploring the shape of the profile log empirical likelihood function and for determining suitable parameterisations for studentised statistics

regression based inverse distance weighting with applications to computer experiments inverse distance weighting idw is a simple method for multivariate interpolation but has poor prediction accuracy in this article we show that the prediction accuracy of idw can be substantially improved by integrating it with a linear regression model this new predictor is quite flexible computationally efficient and works well in problems having high dimensions and or large datasets we also develop a heuristic method for constructing confidence intervals for prediction this article has supplementary material online

screening strategies in the presence of interactions product and process improvement can involve a large number of factors that must be varied simultaneously understanding how factors interact is a key step in identifying those factors that have a substantial impact on the response this article gives the first comprehensive assessment and comparison of screening strategies for interactions using two level supersaturated designs group screening and a variety of data analysis methods including shrinkage regression and bayesian methods we develop novel methodology to allow application of bayesian methods in two stage group screening insights on using the strategies are provided through a variety of simulation scenarios and open issues are discussed supplementary materials are available online

on the second order properties of empirical likelihood with moment restrictions this paper considers the second order properties of empirical likelihood el for a parameter defined by moment restrictions which is the inferential framework of the generalized method of moments it is shown that the el defined for this general framework still admits the delicate second order property of bartlett correction this represents a substantial extension of all the established cases of bartlett correction for the el an empirical bartlett correction is proposed which is shown to work effectively in improving the coverage accuracy of confidence regions for the parameter

an efficient second order linear scheme for the phase field model of corrosive dissolution abstract in this paper we propose an efficient numerical scheme for solving the phase field model pfm of corrosive dissolution that is linear and second order accurate in both time and space the pfm of corrosion is based on the gradient flow of a free energy functional depending on a phase field variable and a single concentration variable while classic backward differentiation formula bdf schemes have been used for time discretization in the literature they require very small time step sizes owing to the strong numerical stiffness and nonlinearity of the parabolic partial differential equation pde system defining the pfm based on the observation that the governing equation corresponding to the phase field variable is very stiff due to the reaction term the key idea of this paper is to employ an exponential time integrator that is more effective for stiff dynamic pdes by combining the exponential integrator based rosenbrock euler scheme with the classic crank nicolson scheme for temporal integration of the spatially semi discretized system we develop a decoupled linear numerical scheme that alleviates the time step size restriction due to high stiffness several numerical examples are presented to demonstrate accuracy efficiency and robustness of the proposed scheme in two dimensions and we find that a time step size of 1 0 3 second for meshes with the typical spatial resolution 1 m is stable additionally the proposed scheme is robust and does not suffer from any convergence issues often encountered by nonlinear newton methods

multivariate statistical process control using lasso this article develops a new multivariate statistical process control spc methodology based on adapting the lasso variable selection method to the spc problem the lasso method has the sparsity property of being able to select exactly the set of nonzero regression coefficients in multivariate regression modeling which is especially useful in cases where the number of nonzero coefficients is small in multivariate spc applications process mean vectors often shift in a small number of components our primary goals are to detect such a shift as soon as it occurs and to identify the shifted mean components using this connection between the two problems we propose a lasso based multivariate test statistic and then integrate this statistic into the multivariate ewma charting scheme for phase ii multivariate process monitoring we show that this approach balances protection against various shift levels and shift directions and thus provides an effective tool for multivariate spc applications this article

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

empirical likelihood in the presence of nuisance parameters summary empirical likelihood was introduced as a nonparametric analogue of ordinary parametric likelihood it is well known that the empirical likelihood ratio statistic inherits a number of properties of the parametric likelihood ratio statistic such as the asymptotic chi squared distribution and bartlett correctability this raises the question of whether or not the same is true in the presence of nuisance parameters recent work by qin lawless 1994 indicates that the chi squared distribution is still valid to first order we show that when nuisance parameters are present as introduced via a system of estimating equations the asymptotic expansion for the signed square root of the empirical likelihood ratio statistic has a nonstandard form this implies that the empirical likelihood ratio statistic itself does not permit a bartlett correction

flux limiting embedded boundary technique for electromagnetic fdtd a general approach for incorporating embedded boundaries into an electromagnetic finite difference time domain fdtd code is presented this algorithm is shown to satisfy gauss s law and enforces no magnetic monopoles while maintaining a globally second order result first order at physical boundaries with no added time step restriction theoretically predicted superior results are shown with an 11 time step reduction from the courant stability limit this is achieved through a physics based flux limiting scheme near physical boundaries stability local truncation error and energy conservation analysis are also provided

a new 3 d conformal pec fdtd scheme with user defined geometric precision and derived stability criterion a new conformal finite difference time domain cfdtd updating scheme for metallic surfaces nonaligned in the grid is presented in this paper in contrast to existing conformal models the new model can be formulated with the original yee fdtd update equation therefore the proposed scheme can be easily added in standard fdtd codes even if the codes are already parallelized or hardware accelerated in addition based on the commonly used conventional stability criterion a derivation of the stability is presented and based on the conformal geometric information a time step reduction formula is presented the time step reduction is used as a user defined parameter to tradeoff speed versus accuracy the achievable geometric precision is optimized to a given time step therefore even with the conventional time step no reduction the presented scheme profits from the conformal discretization to show the performance and the robustness of the proposed scheme canonical validations and two real world applications were investigated a broadband low profile circular antenna was successfully simulated showing the benefit of the conformal fdtd method compared to the conventional scheme furthermore a cad based mobile phone was conformally discretized and successfully simulated showing that the proposed scheme is highly suited for the simulation of advanced engineering problems

a direct approach to sparse discriminant analysis in ultra high dimensions summary sparse discriminant methods based on independence rules such as the nearest shrunken centroids classifier tibshirani et al 2002 and features annealed independence rules fan fan 2008 have been proposed as computationally attractive tools for feature selection and classification with high dimensional data a fundamental drawback of these rules is that they ignore correlations among features and thus could produce misleading feature selection and inferior classification we propose a new procedure for sparse discriminant analysis motivated by the least squares formulation of linear discriminant analysis to demonstrate our proposal we study the numerical and theoretical properties of discriminant analysis constructed via lasso penalized least squares our theory shows that the method proposed can consistently identify the subset of discriminative features contributing to the bayes rule and at the same time consistently estimate the bayes classification direction even when the dimension can grow faster than any polynomial order of the sample size the theory allows for general dependence among features simulated and real data examples show that lassoed discriminant analysis compares favourably with other popular sparse discriminant proposals

interface solutions of partial differential equations with point singularity abstract partial differential equations pdes such as those that describe linear elastic fracture mechanics admit analytic solutions with low regularity at crack tips existing numerical methods for such pdes suffer from the constraint of this low regularity and fail to deliver an optimal high order rate of convergence we approach this problem by i choosing an artificial interface to enclose the center of low regularity and ii representing the solution in the interior of artificial interface as unknown linear combination of known low regularity modes of the solution this results in an interface formulation of the original pde and the linear combination is represented in the interface conditions by enforcing the smooth component of the numerical solution in the interior domain to be approximately zero a least squares problem is obtained for the unknown coefficients the solution of this least squares problem will provide the approximate interface conditions for the numerical solution of the pde in the exterior domain the potential of our interface formulation is favorably demonstrated by numerical experiments on one and two dimensional poisson equations with low regularity solutions high order numerical solutions of unknown coefficients and pdes are obtained this proves the potential of the proposed interface formulation as the theoretical basis for solving linear elastic fracture mechanics problems we address the relations between our interface formulation and domain decomposition methods as well as a regularization strategy for the poisson boltzmann equation with singular charge density

time domain matched interface and boundary mib modeling of debye dispersive media with curved interfaces a new finite difference time domain fdtd method is introduced for solving transverse magnetic maxwell s equations in debye dispersive media with complex interfaces and discontinuous wave solutions based on the auxiliary differential equation approach a hybrid maxwell debye system is constructed which couples the wave equation for the electric component with maxwell s equations for the magnetic components this hybrid formulation enables the calculation of the time dependent parts of the interface jump conditions so that one can track the transient changes in the regularities of the electromagnetic fields across a dispersive interface effective matched interface and boundary mib treatments are proposed to rigorously impose the physical jump conditions which are not only time dependent but also couple both cartesian directions and both magnetic field components based on a staggered yee lattice the proposed mib scheme can deal with arbitrarily curved interfaces and nonsmooth interfaces with sharped edges second order convergences are numerically achieved in solving dispersive interface problems with constant curvatures general curvatures and nonsmooth corners

on bartlett correction of empirical likelihood in the presence of nuisance parameters summary lazar mykland 1999 showed that an empirical likelihood defined by two estimating equations with a nuisance parameter need not be bartlett correctable this paper shows that bartlett correction of empirical likelihood in the presence of a nuisance parameter depends critically on the way the nuisance parameter is removed when formulating the likelihood for the parameter of interest we establish in the broad framework of estimating functions that the empirical likelihood is still bartlett correctable if the nuisance parameter is profiled out given the value of the parameter of interest

a fourth order finite difference method for waveguides with curved perfectly conducting boundaries a novel high order finite difference method is introduced for optical waveguides with smoothly curved perfectly electric conducting pec boundaries the proposed method shares some similarities with our previous matched interface and boundary mib methods developed for treating dielectric interfaces of optical waveguides such as the use of a simple cartesian grid the standard finite difference schemes and fictitious values however the pec boundary conditions have a physical nature quite different from that of the jump conditions at the dielectric interfaces i e all six electric and magnetic field components are prescribed in the jump conditions while only three of them are known at the pec walls consequently the previously developed mib methods are not applicable to deal with the perfectly conducting boundaries to overcome this difficulty a novel ray casting fictitious domain method is constructed to enforce the pec conditions along the normal direction such a boundary implementation couples the transverse magnetic field components so that the resulting ray casting mib method is a full vectorial approach for the modal analysis of optical waveguides the new mib method is validated by considering both homogeneous and inhomogeneous waveguides numerical results confirm the designed fourth order of accuracy

matched interface and boundary mib for the implementation of boundary conditions in high order central finite differences high order central finite difference schemes encounter great difficulties in implementing complex boundary conditions this paper introduces the matched interface and boundary mib method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high order central finite difference schemes to attain arbitrarily high order the mib method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions the proposed approach is extensively validated via boundary value problems initial boundary value problems eigenvalue problems and high order differential equations successful implementations are given to not only dirichlet neumann and robin boundary conditions but also more general ones such as multiple boundary conditions in high order differential equations and time dependent boundary conditions in evolution equations detailed stability analysis of the mib method is carried out the mib method is shown to be able to deliver high order accuracy while maintaining the same or similar stability conditions of the standard high order central difference approximations the application of the proposed mib method to the boundary treatment of other non standard high order methods is also considered

consistent boundary conditions for the yee scheme a new set of consistent boundary conditions for yee scheme approximations of wave equations in two space dimensions are developed and analyzed we show how the classical staircase boundary conditions for hard reflections or in the electromagnetic case conducting surfaces in certain cases give o 1 errors the proposed conditions keep the structure of the yee scheme and are thus well suited for high performance computing the higher accuracy is achieved by modifying the coefficients in the difference stencils near the boundary this generalizes our earlier results with gustafsson and wahlund in one space dimension we study stability and convergence and we present numerical examples

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

bayesian empirical likelihood summary research has shown that empirical likelihood tests have many of the same asymptotic properties as those derived from parametric likelihoods this leads naturally to the possibility of using empirical likelihood as the basis for bayesian inference different ways in which this goal might be accomplished are considered the validity of the resultant posterior inferences is examined as are frequentist properties of the bayesian empirical likelihood intervals

numerical evaluation of hierarchical vector finite elements on curvilinear domains in 2 d when using the finite element method computational efficiency may be improved by using higher order elements typical 2 d triangular rectilinear elements cannot exactly model curved geometries negating the advantage of higher order elements when such geometries are modeled curvilinear elements can be applied to such problems and have significantly better computational efficiency than rectilinear elements when higher order elements are used results are shown for elemental basis orders ranging from ct ln through full fifth order in rectilinear and curvilinear domains

high order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources this paper introduces a novel high order interface scheme the matched interface and boundary mib method for solving elliptic equations with discontinuous coefficients and singular sources on cartesian grids by appropriate use of auxiliary line and or fictitious points physical jump conditions are enforced at the interface unlike other existing interface schemes the proposed method disassociates the enforcement of physical jump conditions from the discretization of the differential equation under study to construct higher order interface schemes the proposed mib method bypasses the major challenge of implementing high order jump conditions by repeatedly enforcing the lowest order jump conditions the proposed mib method is of arbitrarily high order in principle in treating straight regular interfaces we construct mib schemes up to 16th order for more general elliptic problems with curved irregular interfaces and boundary up to 6th order mib schemes have been demonstrated by employing the standard high order finite difference schemes to discretize the laplacian the present mib method automatically reduces to the standard central difference scheme when the interface is absent the immersed interface method iim is regenerated for a comparison study of the proposed method the robustness of the mib method is verified against the large magnitude of the jump discontinuity across the interface the nature of high efficiency and low memory requirement of the mib method is extensively validated via solving various elliptic immersed interface problems in two and three dimensions ee dimensions

calibration and empirical bayes variable selection for the problem of variable selection for the normal linear model selection criteria such as aic c p bic and ric have fixed dimensionality penalties such criteria are shown to correspond to selection of maximum posterior models under implicit hyperparameter choices for a particular hierarchical bayes formulation based on this calibration we propose empirical bayes selection criteria that use hyperparameter estimates instead of fixed choices for obtaining these estimates both marginal and conditional maximum likelihood methods are considered as opposed to traditional fixed penalty criteria these empirical bayes criteria have dimensionality penalties that depend on the data their performance is seen to approximate adaptively the performance of the best fixed penalty criterion across a variety of orthogonal and nonorthogonal set ups including wavelet regression empirical bayes shrinkage estimators of the selected coefficients are also proposed

simulated annealing model search for subset selection in screening experiments the analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large the number of trials is small and there are constraints on model structure common subset selection methods do not perform well in this setting we propose a new approach particularly well suited to screening the method uses an intentionally nonconvergent stochastic search to generate a large set of well fitting models each with the same number of variables model selection is then viewed as a feature extraction problem from this set an easy to use graphical method and an automatic approach are proposed to determine the best models computer code and additional supplementary materials are available online

empirical likelihood for linear models empirical likelihood is a nonparametric method of inference it has sampling properties similar to the bootstrap but where the bootstrap uses resampling it profiles a multinomial likelihood supported on the sample its properties in i i d settings have been investigated in works by owen by hall and by diciccio hall and romano this article extends the method to regression problems fixed and random regressors are considered as are robust and heteroscedastic regressions to make the extension three variations on the original idea are considered it is shown that when some functionals of the distribution of the data are known one can get sharper inferences on other functionals by imposing the known values as constraints on the optimization the result is first order equivalent to conditioning on a sample value of the known functional the use of a euclidean alternative to the likelihood function is investigated a triangular array version of the empirical likelihood theorem is given the one way anova and heteroscedastic regression models are considered in detail an example is given in which inferences are drawn on the parameters of both the regression function and the conditional variance model

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

a bayesian approach to the design and analysis of fractionated experiments specifying a prior distribution for the large number of parameters in the statistical model is a critical step in a bayesian approach to the design and analysis of experiments this article shows that the prior distribution can be induced from a functional prior on the underlying transfer function the functional prior requires specification of only a few hyperparameters and thus can be easily implemented in practice the usefulness of the approach is demonstrated through the analysis of some experiments the article also proposes a new class of design criteria and establishes their connections with the minimum aberration criterion

the risk inflation criterion for multiple regression a new criterion is proposed for the evaluation of variable selection procedures in multiple regression this criterion which we call the risk inflation is based on an adjustment to the risk essentially the risk inflation is the maximum increase in risk due to selecting rather than knowing the correct predictors a new variable selection procedure is obtained which in the case of orthogonal predictors substantially improves on aic c p and bic and is close to optimal in contrast to aic c p and bic which use dimensionality penalties of 2 2 and log n respectively this new procedure uses a penalty 2 log p where p is the number of available predictors for the case of nonorthogonal predictors bounds for the optimal penalty are obtained

variable selection with the strong heredity constraint and its oracle property in this paper we extend the lasso method tibshirani 1996 for simultaneously fitting a regression model and identifying important interaction terms unlike most of the existing variable selection methods our method automatically enforces the heredity constraint that is an interaction term can be included in the model only if the corresponding main terms are also included in the model furthermore we extend our method to generalized linear models and show that it performs as well as if the true model were given in advance that is the oracle property as in fan and li 2001 and fan and peng 2004 the proof of the oracle property is given in online supplemental materials numerical results on both simulation data and real data indicate that our method tends to remove irrelevant variables more effectively and provide better prediction performance than previous work yuan joseph and lin 2007 and zhao rocha and yu 2009 as well as the classical lasso method

additive heredity model for the analysis of mixture of mixtures experiments the mixture of mixtures mom experiment is different from the classical mixture experiment in that the mixture component in mom experiments known as the major component is made up of subcomponen

a new boundary closure scheme for the multiresolution time domain mrtd method this paper introduces a novel boundary closure treatment for the wavelet based multiresolution time domain mrtd solution of maxwell s equations accommodating non trivial boundary conditions such as the robin condition or time dependent condition has been a challenging issue in the mrtd analysis of wave scattering radiation and propagation a matched interface and boundary mib method is introduced to overcome this difficulty several numerical benchmark tests are carried out to validate the mib boundary scheme the proposed boundary treatment can also be applied to other high order finite difference time domain fdtd approaches such as the dispersion relation preserving drp method the mib boundary scheme greatly enhances the feasibility for applying the mrtd methods to more complicated electromagnetic structures

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

higher order frequency domain computational electromagnetics a review of the higher order computational electromagnetics cem for antenna wireless and microwave engineering applications is presented higher order cem techniques use current field basis functions of higher orders defined on large e g on the order of a wavelength in each dimension curvilinear geometrical elements which greatly reduces the number of unknowns for a given problem the paper reviews all major surface volume integral and differential equation electromagnetic formulations within a higher order computational framework focusing on frequency domain solutions with a systematic and unified review of generalized curved parametric quadrilateral triangular hexahedral and tetrahedral elements and various types of higher order hierarchical and interpolatory vector basis functions in both divergence and curl conforming arrangements a large number of actual higher order techniques representing various combinations of formulations elements bases and solution procedures are identified and discussed the examples demonstrate the accuracy efficiency and versatility of higher order techniques and their advantages over low order discretizations the most important one being a much faster higher order convergence of the solution it is demonstrated that both components of the higher order modeling namely higher order geometrical modeling and higher order current field modeling are essential for accurate and efficient cem analysis of general antenna scattering and microwave structures

factor selection and structural identification in the interaction anova model when faced with categorical predictors and a continuous response the objective of an analysis often consists of two tasks finding which factors are important and determining which levels of the factors differ significantly from one another often times these tasks are done separately using analysis of variance anova followed by a post hoc hypothesis testing procedure such as tukey s honestly significant difference test when interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem when testing for differences between two levels of a factor claiming no difference would refer not only to equality of main effects but also to equality of each interaction involving those levels this structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models this article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity type constraint on the model an appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero it is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand we also discuss the application to estimating interactions in the unreplicated case simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint the method is also illustrated using a real data example

a new high order dispersive fdtd method for drude material with complex interfaces in this paper motivated by the needs of tracking the transient change in the regularity of the electromagnetic fields across a drude interface we propose a new maxwell drude formulation for transverse magnetic problems with inhomogeneous drude dispersive materials based on the auxiliary differential equation approach the proposed formulation couples the wave equation for the electric component with maxwell s equations for the magnetic components a new finite difference time domain fdtd algorithm is introduced for solving the proposed maxwell drude system in which the time dependent jump conditions across the drude interface are enforced through the matched interface and boundary mib method the proposed fdtd method achieves a second order of accuracy in solving drude interfaces with fluctuating curvatures and non smooth corners based on a simple yee lattice while it can be generalized to up to sixth order in dealing with a straight drude interface therefore the proposed fdtd method is more accurate and cost efficient than the classical fdtd methods for drude material with complex interfaces

on adjustments based on the signed root of the empirical likelihood ratio statistic summary the standard multivariate normal approximation to the distribution of the signed root of the empirical likelihood ratio statistic is considered in cases where inference is required for a smooth function of the mean of the distribution from which the sample is drawn the error in this approximation is of order o n 2 where n is the sample size and it is shown that the error can be reduced to order o n 1 by using a mean adjustment when a scalar parameter is of interest use of the mean adjustment produces confidence intervals whose endpoints each have coverage error of order o n 1 this is in contrast to use of the unadjusted signed root or equivalently use of the chi squared approximation for the empirical likelihood ratio statistic which produces one sided limits having coverage error of order 0 n 2 for a vector parameter of interest a procedure asymptotically equivalent to the mean adjustment is developed that avoids explicit calculation of the signed square root it is argued for the scalar parameter case that the coverage error of one sided limits can be further reduced to o n 312 by use of both mean and variance adjustments the variance adjustment is given in the case when a scalar mean is of interest the coverage accuracy of confidence limits obtained by the various methods is illustrated by simulation

on empirical likelihood statistical functions abstract we consider the empirical likelihood method for estimation of distribution and quantile functions where side information is incorporated through moment conditions we systematically study the asymptotic properties of the estimators such as the uniform strong laws of large numbers and weak convergence over classes of functions two monte carlo examples are also given to illustrate the practical utility of the method

an improved immersed boundary finite difference method for seismic wave propagation modeling with arbitrary surface topography abstractto accurately simulate seismic wave propagation for the purpose of developing modern land data processing tools especially full waveform inversion fwi we have developed an efficient high order finite difference forward modeling algorithm with the capability of handling arbitrarily shaped free surface topography unlike most existing forward modeling algorithms using curvilinear grids to fit irregular surface topography this finite difference algorithm based on an improved immersed boundary method uses a regular cartesian grid system without suffering from staircasing error which is inevitable in a conventional finite difference method in this improved immersed boundary finite difference ibfd algorithm arbitrarily curved surface topography is accounted for by imposing the free surface boundary conditions at exact boundary locations instead of using body conforming grids or refined grids near the boundaries thus greatly reducing the complexity of its preprocessing procedures and the com

gel estimation and tests of spatial autoregressive models abstract this paper considers the generalized empirical likelihood gel estimation and tests of high order spatial autoregressive sar models by exploring an inherent martingale structure the gel estimator has the same asymptotic distribution as the generalized method of moments estimator explored with same moment conditions for estimation but circumvents a first step estimation of the optimal weighting matrix with a preliminary estimator and thus can be robust to unknown heteroskedasticity and non normality while the gel removes the asymptotic bias from the preliminary estimator and partially removes the bias due to the correlation between the moment conditions and their jacobian the empirical likelihood as a special member of gels further partially removes the bias from estimating the second moment matrix we also formulate the gel overidentification test moran s i test and gel ratio tests for parameter restrictions and non nested hypotheses while some of the conventional tests might not be robust to non normality and or unknown heteroskedasticity the corresponding gel tests can be robust

an efficient variable selection approach for analyzing designed experiments the analysis of experiments in which numerous potential variables are examined is driven by the principles of effect sparsity effect hierarchy and effect heredity we propose an efficient variable selection strategy to specifically address the unique challenges faced by such analysis the proposed methods are natural extensions of the lars general purpose variable selection algorithm they can be computed very rapidly and can find sparse models that better satisfy the goals of experiments simulations and real examples are used to illustrate the wide applicability of the proposed methods

high order fdtd methods for transverse magnetic modes with dispersive interfaces a new finite difference time domain fdtd algorithm is introduced to solve two dimensional 2d transverse magnetic tm modes with a straight dispersive interface driven by the consideration of simplifying interface jump conditions the auxiliary differential equation of the debye constitution model is rewritten to form a new debye maxwell tm system interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface the resulting time dependent jump conditions are rigorously enforced in the fdtd discretization by means of a matched interface and boundary scheme higher order convergences are numerically achieved for the first time in the literature in 2d fdtd simulations of dispersive inhomogeneous media

efficient robust regression via two stage generalized empirical likelihood large and finite sample efficiency and resistance to outliers are the key goals of robust statistics although often not simultaneously attainable we develop and study a linear regression estimator that comes close efficiency is obtained from the estimator s close connection to generalized empirical likelihood and its favorable robustness properties are obtained by constraining the associated sum of weighted squared residuals we prove maximum attainable finite sample replacement breakdown point and full asymptotic efficiency for normal errors simulation evidence shows that compared to existing robust regression estimators the new estimator has relatively high efficiency for small sample sizes and comparable outlier resistance the estimator is further illustrated and compared to existing methods via application to a real dataset with purported outliers

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

adaptive model selection most model selection procedures use a fixed penalty penalizing an increase in the size of a model these nonadaptive selection procedures perform well only in one type of situation for instance bayesian information criterion bic with a large penalty performs well for small models and poorly for large models and akaike s information criterion aic does just the opposite this article proposes an adaptive model selection procedure that uses a data adaptive complexity penalty based on a concept of generalized degrees of freedom the proposed procedure combining the benefit of a class of nonadaptive procedures approximates the best performance of this class of procedures across a variety of different situations this class includes many well known procedures such as aic bic mallows s cp and risk inflation criterion ric the proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression simulation results and an asymptotic

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved