a comparison of two model averaging techniques with an application to growth empirics parameter estimation under model uncertainty is a difficult and fundamental issue in econometrics this paper compares the performance of various model averaging techniques in particular it contrasts bayesian model averaging bma currently one of the standard methods used in growth empirics with a new method called weighted average least squares wals the new method has two major advantages over bma its computational burden is trivial and it is based on a transparent definition of prior ignorance the theory is applied to and sheds new light on growth empirics where a high degree of model uncertainty is typically present

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

forecasting with model uncertainty representations and risk reduction we consider forecasting with uncertainty about the choice of predictor variables the researcher wants to select a model estimate the parameters and use the parameter estimates for forecasting we investigate the distributional properties of a number of different schemes for model choice and parameter estimation in sample model selection using the akaike information criterion out ofsample model selection and splitting the data into subsamples for model selection and parameter estimation using a weak predictor local asymptotic scheme we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks we develop a simulation procedure that improves the accuracy of the out of sample and split sample methods uniformly over the local parameter space we also examine how bootstrap aggregation bagging affects the local asymptotic risk of the estimators and their associated forecasts numerically we find that for many values of the local parameter the out of sample and split sample schemes perform poorly if implemented in the conventional way but they perform well if implemented in conjunction with our risk reduction method or bagging

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

random calibration with many measurements an application of stein estimation in the problem considered a vector of many imprecise measurements e g spectroscopic is used to linearly predict a quantity whose precise measurement is difficult or expensive the regression vector is estimated from a calibration experiment having both types of measurements for a random sample most previous approaches to this problem adjust for approximate multicollinearity which often results from the correlations among the imprecise measurements by inverting an approximation e g factor analytic to their covariance matrix in the approach here it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix it is then estimated by applying a stein contraction of the least squares estimator to the principal components regression estimator examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation

blow up problems for the heat equation with a local nonlinear neumann boundary condition abstract this paper estimates the blow up time for the heat equation u t u with a local nonlinear neumann boundary condition the normal derivative u n u q on 1 one piece of the boundary while on the rest part of the boundary u n 0 the motivation of the study is the partial damage to the insulation on the surface of space shuttles caused by high speed flying subjects we show the finite time blow up of the solution and estimate both upper and lower bounds of the blow up time in terms of the area of 1 in many other work they need the convexity of the domain and only consider the problem with 1 in this paper we remove the convexity condition and only require to be c 2 in addition we deal with the local nonlinearity namely 1 can be just part of

a convex concave problem with a nonlinear boundary condition in this paper we study the existence of nontrivial solutions of the problem u u u p 2uin u u q 2uon with 1 q 2 n 1 n 2 and 1 p 2n n 2 in the concave convex case i e 1 q 2 p if is small there exist two positive solutions while for large there is no positive solution when p is critical and q subcritical we obtain existence results using the concentration compactness method finally we apply the implicit function theorem to obtain solutions for small near u0 1

how far are automatically chosen regression smoothing parameters from their optimum abstract we address the problem of smoothing parameter selection for nonparametric curve estimators in the specific context of kernel regression estimation call the optimal bandwidth the minimizer of the average squared error we consider several automatically selected bandwidths that approximate the optimum how far are the automatically selected bandwidths from the optimum the answer is studied theoretically and through simulations the theoretical results include a central limit theorem that quantifies the convergence rate and gives the differences asymptotic distribution the convergence rate turns out to be excruciatingly slow this is not too disappointing because this rate is of the same order as the convergence rate of the difference between the minimizers of the average squared error and the mean average squared error in some simulations by john rice the selectors considered here performed quite differently from each other we anticipated that these differences would be reflected in differ

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

global blow up for a localized nonlinear parabolic equation with a nonlocal boundary condition abstract this paper deals with the blow up properties of positive solutions to a nonlinear parabolic equation with a localized reaction source and a nonlocal boundary condition under certain conditions the blowup criteria is established furthermore when f u u p 0 p 1 the global blowup behavior is shown and the blowup rate estimates are also obtained

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

forecasting using random subspace methods textabstractrandom subspace methods are a novel approach to obtain accurate forecasts in high dimensional regression settings we provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables we focus on two approaches the first is random subset regression where random subsets of predictors are used to construct a forecast second we discuss random projection regression where artificial predictors are formed by randomly weighting the original predictors using recent results from random matrix theory we obtain a tight bound on the mean squared forecast error for both randomized methods we identify settings in which one randomized method results in more precise forecasts than the other and than alternative regularization strategies such as principal component regression partial least squares lasso and ridge regression the predictive accuracy on the high dimensional macroeconomic fred md data set increases substantially when using the randomized methods with random subset regression outperforming any one of the above mentioned competing methods for at least 66 of the series

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

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

lattice boltzmann simulation of pattern formation under cross diffusion in this paper a lattice boltzmann model for cross reaction diffusion system is proposed in order to recover the cross diffusion equations by lattice boltzmann method we transform the equations into a complex reaction diffusion equation this complex reaction diffusion equation is recovered with higher order accuracy of the truncation error based on this model two typical reaction diffusion systems with cross diffusion predator prey system and inhomogeneous brusselator model are simulated the numerical results show that this model can be used to simulate the cross reaction diffusion systems

range image segmentation using surface selection criterion in this paper we address the problem of recovering the true underlying model of a surface while performing the segmentation first and in order to solve the model selection problem we introduce a novel criterion which is based on minimising strain energy of fitted surfaces we then evaluate its performance and compare it with many other existing model selection techniques using this criterion we then present a robust range data segmentation algorithm capable of segmenting complex objects with planar and curved surfaces the presented algorithm simultaneously identifies the type order and geometric shape of each surface and separates all the points that are part of that surface this paper includes the segmentation results of a large collection of range images obtained from objects with planar and curved surfaces the resulting segmentation algorithm successfully segments various possible types of curved objects more importantly the new technique is capable of detecting the association between separated parts of a surface which has the same cartesian equation while segmenting a scene this aspect is very useful in some industrial applications of range data analysis

regularized liml for many instruments the use of many moment conditions improves the asymptotic efficiency of the instrumental variables estimators however in finite samples the inclusion of an excessive number of moments increases the bias to solve this problem we propose regularized versions of the limited information maximum likelihood liml based on three different regularizations tikhonov landweber fridman and principal components our estimators are consistent and asymptotically normal under heteroskedastic error moreover they reach the semiparametric efficiency bound assuming homoskedastic error we show that the regularized liml estimators possess finite moments when the sample size is large enough the higher order expansion of the mean square error mse shows the dominance of regularized liml over regularized two staged least squares estimators we devise a data driven selection of the regularization parameter based on the approximate mse a monte carlo study and two empirical applications illustrate the relevance of our estimators

improvements on lower bounds for the blow up time under local nonlinear neumann conditions abstract this paper studies the heat equation u t u in a bounded domain r n n 2 with positive initial data and a local nonlinear neumann boundary condition the normal derivative u n u q on partial boundary 1 for some q 1 while u n 0 on the other part we investigate the lower bound of the blow up time t of u in several aspects first t is proved to be at least of order q 1 1 as q 1 since the existing upper bound is of order q 1 1 this result is sharp secondly if is convex and 1 denotes the surface area of 1 then t is shown to be at least of order 1 1 n 1 for n 3 and 1 1 ln 1 1 for n 2 as 1 0 while the previous result is 1 for any 1 n 1 finally we generalize the results for convex domains to the domains with only local convexity near 1

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

finite volume element approximation of an inhomogeneous brusselator model with cross diffusion this paper is concerned with the study of pattern formation for an inhomogeneous brusselator model with cross diffusion modeling an autocatalytic chemical reaction taking place in a three dimensional domain for the spatial discretization of the problem we develop a novel finite volume element fve method associated to a piecewise linear finite element approximation of the cross diffusion system we study the main properties of the unique equilibrium of the related dynamical system a rigorous linear stability analysis around the spatially homogeneous steady state is provided and we address in detail the formation of turing patterns driven by the cross diffusion effect in addition we focus on the spatial accuracy of the fve method and a series of numerical simulations confirm the expected behavior of the solutions in particular we show that depending on the spatial dimension the magnitude of the cross diffusion influences the selection of spatial patterns

the balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation abstract we study nonnegative solutions of u t u m xx x t 0 l 0 t u m x 0 t u p 0 t t 0 t u m x l t u q l t t 0 t u x 0 u 0 x x 0 l where m p q and l are positive parameters for different values of the parameters three situations may occur 1 all solutions of this problem exist for all t 0 2 for certain initial data functions the solution exists for all t 0 while for others the solution blows up as t t for some finite t 3 excepting the trivial solution when u0 0 all solutions blow up as t t for some finite t we identify in terms of the parameters which of them actually happens for solutions which blow up we find the blow up rate and the blow up set

two nonparametric methods for identifying the impulse response of linear systems this paper addresses the problem of impulse response identification using nonparametric methods although the techniques developed herein apply to the truncated untruncated and circulant models we focus on the truncated model which is useful in certain applications two methods of impulse response identification will be presented the first is based on the minimization of the c l statistic which is an estimate of the mean square prediction error the second is a bayesian approach for both of these methods we consider the effects of using both the identity matrix and the laplacian matrix as weights on the energy in the impulse response in addition we present a method for estimating the effective length of the impulse response estimating the length is particularly important in the truncated case finally we develop a method for estimating the noise variance at the output which is needed in the approach involving the c l statistic often prior information on the noise variance is not available and a good estimate is crucial to the success of estimating the impulse response with a nonparametric technique

toward optimal model averaging in regression models with time series errors abstract consider a regression model with infinitely many parameters and time series errors we are interested in choosing weights for averaging across generalized least squares gls estimators obtained from a set of approximating models however gls estimators depending on the unknown inverse covariance matrix of the errors are usually infeasible we therefore construct feasible generalized least squares fgls estimators using a consistent estimator of the unknown inverse matrix based on this inverse covariance matrix estimator and fgls estimators we develop a feasible autocovariance corrected mallows model averaging criterion to select weights thereby providing an fgls model averaging estimator of the true regression function we show that the generalized squared error loss of our averaging estimator is asymptotically equivalent to the minimum one among those of gls model averaging estimators with the weight vectors belonging to a continuous set which includes the discrete weight set used in hansen 2007 as its proper subset

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

turing pattern formation in the brusselator model with superdiffusion the effect of superdiffusion on pattern formation and pattern selection in the brusselator model is studied our linear stability analysis shows in particular that unlike the case of normal diffusion the turing instability can occur even when diffusion of the inhibitor is slower than that of the initiator a weakly nonlinear analysis yields a system of amplitude equations analysis of which predicts parameter regimes where hexagons stripes and their coexistence are expected numerical computations of the original brusselator model near the stability boundaries confirm the results of the analysis in addition further from the stability boundaries we find a regime of self replicating spots

model selection an integral part of inference we argue that model selection uncertainty should be fully incorporated into statistical inference whenever estimation is sensitive to model choice and that choice is made with reference to the data we consider different philosophies for achieving this goal and suggest strategies for data analysis we illustrate our methods through three examples the first is a poisson regression of bird counts in which a choice is to be made between inclusion of one or both of two covariates the second is a line transect data set for which different models yield substantially different estimates of abundance the third is a simulated example in which truth is known

oracle inequalities for inverse problems we consider a sequence space model of statistical linear inverse problems where we need to estimate a function f from indirect noisy observations let a finite set a of linear estimators be given our aim is to mimic the estimator in a that has the smallest risk on the true f under general conditions we show that this can be achieved by simple minimization of an unbiased risk estimator provided the singular values of the operator of the inverse problem decrease as a power law the main result is a nonasymptotic oracle inequality that is shown to be asymptotically exact this inequality can also be used to obtain sharp minimax adaptive results in particular we apply it to show that minimax adaptation on ellipsoids in the multivariate anisotropic case is realized by minimization of unbiased risk estimator without any loss of efficiency with respect to optimal nonadaptive procedures

piecewise polynomial estimation of a regression function we deal with the problem of choosing a piecewise polynomial estimator of a regression function s mapping 0 1 p into r in a first part of this paper we consider some collection of piecewise polynomial models each model is defined by a partition m of 0 1 p and a series of degrees d d j j m nm we propose a penalized least squares criterion which selects a model whose associated piecewise polynomial estimator performs approximately as well as the best one in the sense that its quadratic risk is close to the infimum of the risks the risk bound we provide is nonasymptotic in a second part we apply this result to tree structured collections of partitions which look like the one constructed in the first step of the cart algorithm and we propose an extension of the cart algorithm to build a piecewise polynomial estimator of a regression function

existence of spatial patterns in a predator prey model with self and cross diffusion in this work we investigate the spatiotemporal dynamics of reaction diffusion equations subject to cross diffusion in the frame of a two dimensional ratio dependent predator prey model the conditions for diffusion driven instability are obtained and the turing space in the parameters space is achieved moreover the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings different types of spatial patterns through diffusion driven instability of the proposed model are portrayed and analysed lastly the paper finishes with an external discussion of biological relevance of the analysis regarding cross diffusion and pattern issues

why bandwidth selectors tend to choose smaller bandwidths and a remedy summary this note is concerned with the problem of automatic data driven bandwidth selectors for nonparametric regression though some selectors were shown to be consistent and asymptotically unbiased by rice 1984 and hardle hall marron 1988 it is often observed in simulation studies that most selectors are biased toward undersmoothing an explanation for this is given the source of the large sample variation in the bandwidth estimates is also pointed out this leads to the consideration of a new procedure which is a simple modification of a classical selector a simulation study suggests that the proposed selector is much more consistent than the classical one

blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition abstract in this paper we study the large time behavior of positive solutions of the heat equation under the nonlinear boundary condition u f u where is the outward normal and f is nondecreasing with f u 0 for u 0 we show that if b r and 1 f is integrable at infinity there is finite time blow up for any initial datum in the two dimensional case we show that this is true for any smooth simply connected domain in the radially symmetric case if f c2 is convex and satisfies the properties above we show that blow up occurs only at the boundary

lattice boltzmann method for non newtonian power law fluids we study an ad hoc extension of the lattice boltzmann method that allows the simulation of non newtonian fluids described by generalized newtonian models we extensively test the accuracy of the method for the case of shear thinning and shear thickening truncated power law fluids in the parallel plate geometry and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution finally we also tested the method in the reentrant flow geometry in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points in this geometry we also found excellent agreement with the solutions obtained by standard finite element methods and the agreement improves with higher lattice resolution

relative rates of convergence for efficient model selection criteria in linear regression summary two approaches to estimating a smooth regression function not specified by a finite number of parameters are i to fit a parametric model to the data with the number of parameters selected by the akaike information criterion aic and ii to use nonparametric smoothing techniques with the smoothing parameter selected by cross validation or some other automatic method we consider the relative rate of convergence of the mean integrated squared error of the selected estimator compared to the best possible estimator in the class of candidates under consideration we extend results of shibata 1981 to show that the relative rate of convergence using aic in the parametric case can be as fast as op n for arbitrary positive d we also show that this rate can be attained in the special cases of polynomial and trigonometric regression

optimal bounds for aggregation of affine estimators we study the problem of aggregation of estimators when the estimators are not independent of the data used for aggregation and no sample splitting is allowed if the estimators are deterministic vectors it is well known that the minimax rate of aggregation is of order log m where m is the number of estimators to aggregate it is proved that for affine estimators the minimax rate of aggregation is unchanged it is possible to handle the linear dependence between the affine estimators and the data used for aggregation at no extra cost the minimax rate is not impacted either by the variance of the affine estimators or any other measure of their statistical complexity the minimax rate is attained with a penalized procedure over the convex hull of the estimators for a penalty that is inspired from the q aggregation procedure the results follow from the interplay between the penalty strong convexity and concentration

three dimensional multi relaxation time mrt lattice boltzmann models for multiphase flow in this paper three dimensional 3d multi relaxation time mrt lattice boltzmann lb models for multiphase flow are presented in contrast to the bhatnagar gross krook bgk model a widely employed kinetic model in mrt models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted as a result the mrt models offer a significant improvement in numerical stability of the lb method for simulating fluids with lower viscosities we show through the chapman enskog multiscale analysis that the continuum limit behavior of 3d mrt lb models corresponds to that of the macroscopic dynamical equations for multiphase flow we extend the 3d mrt lb models developed to represent multiphase flow with reduced compressibility effects the multiphase models are evaluated by verifying the laplace young relation for static drops and the frequency of oscillations of drops the results show satisfactory agreement with available data and significant gains in numerical stability

parametric or nonparametric a parametricness index for model selection in model selection literature two classes of criteria perform well asymptotically in different situations bayesian information criterion bic as a representative is consistent in selection when the true model is finite dimensional parametric scenario akaike s information criterion aic performs well in an asymptotic efficiency when the true model is infinite dimensional nonparametric scenario but there is little work that addresses if it is possible and how to detect the situation that a specific model selection problem is in in this work we differentiate the two scenarios theoretically under some conditions we develop a measure parametricness index pi to assess whether a model selected by a potentially consistent procedure can be practically treated as the true model which also hints on aic or bic is better suited for the data for the goal of estimating the regression function a consequence is that by switching between aic and bic based on the pi the resulting regression estimator is simultaneously asymptotically efficient for both parametric and nonparametric scenarios in addition we systematically investigate the behaviors of pi in simulation and real data and show its usefulness

roughness and cavitations effects on electro osmotic flows in rough microchannels using the lattice poisson boltzmann methods this paper investigates the effects of roughness and cavitations in microchannels on the electro osmotic flow behaviors using the lattice poisson boltzmann methods which combined one lattice evolution method for solving the non linear poisson boltzmann equation for electric potential distribution with the other lattice evolution method for solving the navier stokes equations for fluid flow the boundary conditions are correctly treated for consistency between the both the results show that for the electro osmotic flows in homogeneously charged rough channels the flow rate does not vary with the roughness height or the interval space monotonically the flow rate varies slightly with the roughness height or even increases a little when the roughness is very small and then decreases when the roughness height is larger than 5 channel width the flow rate decreases first and then increase with the roughness interval space an interval space at twice roughness width makes the flow rate minimum for the heterogeneously charged rough channel the flow rate increases with the roughness surface potential at a super linear rate for the electro osmotic flows in microchannels with cavitations the flow rate change little with the cavitations depth when the depth value is very low and decreases sharply when the depth is greater than 3 channel width the flow rate trends to be a constant when the cavitations are very deep the flow rate decreases with the cavitations width but increases with the cavitations interval

bandwidth selection for indirect density estimation based on corrupted histogram data abstract motivated by a number of practical applications we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts due to variability in the process of correction the histogram cannot be modeled in terms of simple scaled poisson statistics this departure necessitates the development of a new methodology for bandwidth selection a variant of the method of unbiased risk estimation is proposed the methodology is studied using numerical simulations and asymptotic analysis tools in the context of a class of idealized density deconvolution problems the methodology is adapted for application to the practical reconstruction problem of positron emission tomography pet realistic numerical simulations and physical phantom data are presented to validate the approach in this setting some illustrations with cerebral glucose utilization and myocardial blood flow studies from some actual patient data sets

nonparametric variable selection the earth algorithm we consider regression experiments involving a response variable y and a large number of predictor variables x1 xd many of which may be irrelevant for the prediction of y and thus must be removed before y can be predicted from the x s we consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold in the first of these procedures scores are obtained by randomly drawing subregions tubes of the predictor space that constrain all but one predictor and in each subregion computing a signal to noise ratio efficacy based on a nonparametric univariate regression of y on the unconstrained variable the subregions are adapted to boost weak variables iteratively by searching hunting for the subregions in which the efficacy is maximized the efficacy can be viewed as an approximation to a one to one function of the probability of identif

equivalence between out of sample forecast comparisons and wald statistics we demonstrate the equivalence between a commonly used out of sample test of equal predictive accuracy and the dierence between two wald statistics this equivalence greatly simplies the computational burden of calculating recursive out of sample tests and evaluating their critical values next we show that the limit distribution which has previously been expressed through stochastic integrals has a simple representation in terms of 2 distributed random variables and we derive the density of the limit distribution we also generalize the limit theory to cover local alternatives and characterize the power properties of the test our results shed new light on the test and establish certain weaknesses associated with using out of sample forecast comparison tests to conduct inference about nested regression models

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

parallel performance and accuracy of lattice boltzmann and traditional finite difference methods for solving the unsteady two dimensional burger s equation abstract lattice boltzmann methods are gaining recognition in the field of computational fluid dynamics due to their computational efficiency in order to quantify the computational efficiency and accuracy of the lattice boltzmann method it is compared with efficient traditional finite difference methods such as the alternating direction implicit scheme the lattice boltzmann algorithm implemented in previous studies does not approach peak performance for simulations where the data involved in computation per time step is more than the cache size due to this data is obtained from the main memory and this access is much slower than access to cache memory using a cache optimized lattice boltzmann algorithm this paper takes into account the full computational strength of the lattice boltzmann method the com parison is performed on both a single processor and multiple processors

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

boundary fluxes for nonlocal diffusion abstract we study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary this problem may be seen as a generalization of the usual neumann problem for the heat equation first we prove existence uniqueness and a comparison principle next we study the behavior of solutions for some prescribed boundary data including blowing up ones finally we look at a nonlinear flux boundary condition

linear model selection by cross validation abstract we consider the problem of selecting a model having the best predictive ability among a class of linear models the popular leave one out cross validation method which is asymptotically equivalent to many other model selection methods such as the akaike information criterion aic the c p and the bootstrap is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n we show that the inconsistency of the leave one out cross validation can be rectified by using a leave n v out cross validation with n v the number of observations reserved for validation satisfying n v n 1 as n this is a somewhat shocking discovery because nv n 1 is totally opposite to the popular leave one out recipe in cross validation motivations justifications and discussions of some practical aspects of the use of the leave n v out cross validation method are provided and results