covariance regularization by thresholding this paper considers regularizing a covariance matrix of p variables estimated from n observations by hard thresholding we show that the thresholded estimate is consistent in the operator norm as long as the true covariance matrix is sparse in a suitable sense the variables are gaussian or sub gaussian and log p n 0 and obtain explicit rates the results are uniform over families of covariance matrices which satisfy a fairly natural notion of sparsity we discuss an intuitive resampling scheme for threshold selection and prove a general cross validation result that justifies this approach we also compare thresholding to other covariance estimators in simulations and on an example from climate data 1 introduction estimation of covariance matrices is important in a number of areas of statistical analysis including dimension reduction by principal component analysis pca classification by linear or quadratic discriminant analysis lda and qda establishing independence and conditional independence relations in the context of graphical models and setting confidence intervals on linear functions of the means of the components in recent years many application areas where these tools are used have been dealing with very high dimensional datasets and sample sizes can be very small relative to dimension examples include genetic data brain imaging spectroscopic imaging climate data and many others it is well known by now that the empirical covariance matrix for samples of size n from a p variate gaussian distribution np p is not a good estimator of the population covariance if p is large many results in random matrix theory illustrate this from the classical mary law 29 to the more recent work of johnstone and his students on the theory of the largest eigenvalues 12 23 30 and associated eigenvectors 24 however with the exception of a method for estimating the covariance spectrum 11 these probabilistic results do not offer alternatives to the sample covariance matrix alternative estimators for large covariance matrices have therefore attracted a lot of attention recently two broad classes of covariance estimators have emerged those that rely on a natural ordering among variables and assume that variables

applications of boundary integral equation methods in 3d electromagnetic scattering this paper is concerned with the application of boundary integral equation method to the electromagnetic scattering of a perfect conductor in the three dimensional space a collocation method is employed for the magnetic field integral equation and error estimates are derived far field patterns and radar cross sections are computed for various wave numbers in the case of sphere numerical experiments are compared to those ontained from the mie series method in order to verify the predicted theoretical results

rank based analysis of the heteroscedastic linear model abstract heteroscedasticity often causes problems in the analysis of linear models frequently for such cases scale is a function of the response here for such models a methodology is presented based on well known rank based procedures the procedure is iterative using the residuals from an initial r estimate of the regression coefficients scale is estimated by inverting a linear rank test for scale this in turn leads to a weighted r estimate of the regression coefficients and then to a final estimate of scale asymptotic linearity results for these estimates are derived from which their asymptotic distribution is obtained the weighted r estimate has the same asymptotic distribution as the optimal known scale r estimate hence it is efficiently robust consistent estimates of the standard errors of the r estimates of scale and the regression coefficients are determined based on these results a complete inference for the regression coefficients and the scale parameter is realized including a

unified lasso estimation by least squares approximation we propose a method of least squares approximation lsa for unified yet simple lasso estimation our general theoretical framework includes ordinary least squares generalized linear models quantile regression and many others as special cases specifically lsa can transfer many different types of lasso objective functions into their asymptotically equivalent least squares problems thereafter the standard asymptotic theory can be established and the lars algorithm can be applied in particular if the adaptive lasso penalty and a bayes information criterion type tuning parameter selector are used the resulting lsa estimator can be as efficient as the oracle extensive numerical studies confirm our theory

some new estimation methods for weighted regression where there are possible outliers the problem considered is the robust estimation of the variance parameter in a heteroscedastic linear model we treat the situation in which the variance is a function of the explanatory variables to estimate robustly the variance in this case it is necessary to guard against the influence of outliers in the design as well as outliers in the response by analogy with the homoscedastic regression case we propose two estimators that do this their performances are evaluated on a number of data sets we had considerable success with estimators that bound the self influence that is the influence an observation has on its own fitted value we conjecture that in other situations e g homoscedastic regression bounding the selfinfluence will lead to estimators with good robustness properties

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

three dimensional electromagnetic scattering t matrix computations the infinite t matrix method is a powerful tool for electromagnetic scattering simulations particularly when one is interested in changes in orientation of the scatterer with respect to the incident wave or changes of configuration of multiple scatterers and random particles because it avoids the need to solve the fully reconfigured systems the truncated t matrix for each scatterer in an ensemble is often computed using the null field method the main disadvantage of the null field based t matrix computation is its numerical instability for particles that deviate from a sphere for large and or highly non spherical particles the null field method based truncated t matrix computations can become slowly convergent or even divergent in this work we describe an electromagnetic scattering surface integral formulation for t matrix computations that avoids the numerical instability the new method is based on a recently developed high order surface integral equation algorithm for far field computations using basis functions that are tangential on a chosen non spherical obstacle the main focus of this work is on the mathematical details required to apply the high order algorithm to compute a truncated t matrix that describes the scattering properties of a chosen perfect conductor in a homogeneous medium we numerically demonstrate the stability and convergence of the t matrix computations for various perfect conductors using plane wave incident radiation at several low to medium frequencies and simulation of the associated radar cross of the obstacles

deletion diagnostics for generalised estimating equations summary deletion diagnostics are proposed for generalised estimating equations the diagnostics consider leverage and residuals to measure the influence of a subset of observations on the estimated regression parameters and on the estimated values of the linear predictor computational formulae are provided which correspond to the influence of a single observation and of an entire cluster of correlated observations additionally diagnostics are given which approximate the effect of deletion of an arbitrary subset of observations under a model with general covariance structure and arbitrary link function extending proposition 3 of christensen pearson johnson 1992 the proposed measures are applied to medical data

discrete boundary finite element schemes for an exterior problem for the time harmonic maxwell s equation abstract a general boundary integral formulation using galerkin procedure is applied to compute the scattering electric field produced by the diffraction of an incident electromagnetic wave by a perfectly conducting obstacle this electric field satisfies the three dimensional time harmonic maxwell s equations for which the skin currents and charges are to be approximated using boundary finite element method with the help of linear and quadratic finite elements of lagrange type we introduce an approximate surface on which the discrete formulation is defined and construct approximate surface currents and charges in addition we study the existence and the uniqueness of the solution of the discrete problem and develop some error estimates for the currents and charges numerical results are also presented in order to validate our numerical approach

perturbation and scaled cook s distance cook s cook 1977 distance is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross sectional data however for many complex data structures e g longitudinal data no rigorous approach has been developed to address a fundamental issue deleting subsets with different numbers of observations introduces different degrees of perturbation to the current model fitted to the data and the magnitude of cook s distance is associated with the degree of the perturbation the aim of this paper is to address this issue in general parametric models with complex data structures we propose a new quantity for measuring the degree of the perturbation introduced by deleting a subset we use stochastic ordering to quantify the stochastic relationship between the degree of the perturbation and the magnitude of cook s distance we develop several scaled cook s distances to resolve the comparison of cook s distance for different subset deletions theoretical and numerical examples are examined to highlight the broad spectrum of applications of these scaled cook s distances in a formal influence analysis

on the distribution of the largest eigenvalue in principal components analysis let x 1 denote the square of the largest singular value of an n p matrix x all of whose entries are independent standard gaussian variates equivalently x 1 is the largest principal component variance of the covariance matrix x x or the largest eigenvalue of a p variate wishart distribution on n degrees of freedom with identity covariance consider the limit of large p and n with n p gamma ge 1 when centered by mu p sqrt n 1 sqrt p 2 and scaled by sigma p sqrt n 1 sqrt p 1 sqrt n 1 1 sqrt p 1 3 the distribution of x 1 approaches the tracey widom law of order 1 which is defined in terms of the painleve ii differential equation and can be numerically evaluated and tabulated in software simulations show the approximation to be informative for n and p as small as 5 the limit is derived via a corresponding result for complex wishart matrices using methods from random matrix theory the result suggests that some aspects of large p multivariate distribution theory may be easier to apply in practice than their fixed p counterparts

diagnostics in categorical data analysis diagnostics as measures of model deviations and of the influence of particular data sets are used extensively in modern regression analysis for contingency tables and more generally for the parametric multinomial distribution it is not the influence of individual observations which is of interest but rather the contribution to a lack of model fit or to the values of the parameter estimates from a single cell in the table which must be evaluated hence diagnostics for contingency tables take somewhat different forms

sure independence screening in generalized linear models with np dimensionality ultrahigh dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research among others fan and lv 2008 propose an independent screening framework by ranking the marginal correlations they showed that the correlation ranking procedure possesses a sure independence screening property within the context of the linear model with gaussian covariates and responses in this paper we propose a more general version of the independent learning with ranking the maximum marginal likelihood estimates or the maximum marginal likelihood itself in generalized linear models we show that the proposed methods with fan and lv 2008 as a very special case also possess the sure screening property with vanishing false selection rate the conditions under which that the independence learning possesses a sure screening is surprisingly simple this justifies the applicability of such a simple method in a wide spectrum we quantify explicitly the extent to which the dimensionality can be reduced by independence screening which depends on the interactions of the covariance matrix of covariates and true parameters simulation studies are used to illustrate the utility of the proposed approaches in addition we supported in part by grant nsf grants dms 0714554 and dms 0704337 the bulk of the work was conducted when rui song was a postdoctoral research fellow at princeton university the authors would like to thank the associate editor and two referees for their constructive comments that improve the presentation and the results of the paper ams 2000 subject classifications primary 68q32 62j12 secondary 62e99 60f10

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

regression diagnostics for rank based methods abstract residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model in this article we explore the properties of the residuals from a rank based fit of the model we present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank based fit we show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model furthermore our diagnostic techniques inherit the excellent efficiency properties of the rank based fit over a wide class of error distributions including asymmetric distributions we illustrate these techniques with several examples

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

case deletion measures for models with incomplete data summary this paper proposes several case deletion measures for assessing the influence of an observation for complicated models with real missing data or hypothetical missing data corresponding to latent random variables the idea is to generalise cook s 1977 approach to the conditional expectation of the complete data loglikelihood function in the em algorithm on the basis of the diagnostic measures a procedure is proposed for detecting influential observations two examples illustrate our methodology we show that the method can be applied efficiently to a wide variety of complicated problems that are difficult to handle by existing methods

finite element method for time dependent maxwell s equations based on an explicit magnetic field scheme this paper provides a convergence analysis of the finite element method for time dependent maxwell s equations by means of an explicit magnetic field scheme error estimates in finite time are given and it is verified that provided the time stepsize is sufficiently small the proposed algorithm yields for finite time t an error of o hs in the l2 norm for the electric field e the magnetic field h where h is the mesh size and 1 2 s 1 in addition some numerical results are reported in the paper

fully discrete finite element scheme for maxwell s equations with non linear boundary condition abstract we study a full maxwell s system accompanied with a non linear degenerate boundary condition which represents a generalization of the classical silver muller condition for a non perfect conductor the relationship between the normal components of electric e and magnetic h field obeys the following power law h e 1 e for some 0 1 we establish the existence and uniqueness of a weak solution in a suitable function spaces under the minimal regularity assumptions on the boundary and the initial data e 0 and h 0 we design a non linear time discrete approximation scheme and prove convergence of the approximations to a weak solution we also derive the error estimates for the time discretization as a next step we study the fully discrete problem using curl conforming edge elements and derive the corresponding error estimates finally we present some numerical experiments

influence diagnostics and outlier tests for semiparametric mixed models summary semiparametric mixed models are useful in biometric and econometric applications especially for longitudinal data maximum penalized likelihood estimators mples have been shown to work well by zhang and co workers for both linear coefficients and nonparametric functions this paper considers the role of influence diagnostics in the mple by extending the case deletion and subject deletion analysis of linear models to accommodate the inclusion of a nonparametric component we focus on influence measures for the fixed effects and provide formulae that are analogous to those for simpler models and readily computable with the mple algorithm we also establish an equivalence between the case or subject deletion model and a mean shift outlier model from which we derive tests for outliers the influence diagnostics proposed are illustrated through a longitudinal hormone study on progesterone and a simulated example

influence analysis based on the case sensitivity function the case sensitivity function approach to influence analysis is introduced as a natural smooth extension of influence curve methodology in which both the insights of geometry and the power of convex analysis are available in it perturbation is defined as movement between probability vectors defining weighted empirical distributions a euclidean geometry is proposed giving such perturbations both size and direction the notion of the salience of a perturbation is emphasized this approach has several benefits a general probability case weight analysis results answers to a number of outstanding questions follow directly rescaled versions of the three usual finite sample influence curve measures seen now to be required for comparability across different sized subsets of cases are readily available these new diagnostics directly measure the salience of the infinitesimal perturbations involved their essential unity both within and between subsets is evident geometrically finally it is shown how a relaxation strategy in which a high dimensional 0 ncm discrete problem is replaced by a low dimensional o n continuous problem can combine with convex optimization results to deliver better performance in challenging multiple case influence problems further developments are briefly indicated

forward regression for ultra high dimensional variable screening motivated by the seminal theory of sure independence screening fan and lv 2008 sis we investigate here another popular and classical variable screening method namely forward regression fr our theoretical analysis reveals that fr can identify all relevant predictors consistently even if the predictor dimension is substantially larger than the sample size in particular if the dimension of the true model is finite fr can discover all relevant predictors within a finite number of steps to practically select the best candidate from the models generated by fr the recently proposed bic criterion of chen and chen 2008 can be used the resulting model can then serve as an excellent starting point from where many existing variable selection methods e g scad and adaptive lasso can be applied directly fr s outstanding finite sample performances are confirmed by extensive numerical studies

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

some notes on singular integral techniques in boundary element analysis the paper presented here reviews the numerical techniques used currently to calculate the singular integrals and nearly singular integrals in the boundary element analysis some incorrect algorithms published before are discussed and a new numerical technique to calculate the nearly singular integral is developed the numerical results show a significant improvement in both accuracy and efficiency compared to the traditional adaptive gaussian quadrature and subdivision techniques

duality estimates for the numerical solution of integral equations we formulate and prove aubin nitsche type duality estimates for the error of general projection methods examples of applications include collocation methods and augmented galerkin methods for boundary integral equations on plane domains with corners and three dimensional screen and crack problems for some of these methods we obtain higher order error estimates in negative norms in cases where previous formulations of the duality arguments were not applicable

adaptive lasso for cox s proportional hazards model summary we investigate the variable selection problem for cox s proportional hazards model and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience the new method is based on a penalized log partial likelihood with the adaptively weighted l1 penalty on regression coefficients providing what we call the adaptive lasso estimator the method incorporates different penalties for different coefficients unimportant variables receive larger penalties than important ones so that important variables tend to be retained in the selection process whereas unimportant variables are more likely to be dropped theoretical properties such as consistency and rate of convergence of the estimator are studied we also show that with proper choice of regularization parameters the proposed estimator has the oracle properties the convex optimization nature of the method leads to an efficient algorithm both simulated and real examples show that the method performs competitively

a hybrid high order algorithm for radar cross section computations we describe a high order method for computing the monostatic and bistatic radar cross section rcs of a class of three dimensional targets our method is based on an electric field surface integral equation reformulation of the maxwell equations the hybrid nature of the scheme is due to approximations based on a combination of tangential and nontangential basis functions on a parametric reference spherical surface a principal feature of the high order algorithm is that it requires solutions of linear systems with substantially fewer unknowns than existing methods we demonstrate that very accurate rcs values for medium electromagnetic sized scatterers can be computed using a few tens of thousands of unknowns thus linear systems arising in the high order method for low to medium frequency scattering can be solved using direct solves this is extremely advantageous in monostatic rcs computations for which transmitters and receivers are co located and hence the discretized electromagnetic linear system must be solved for hundreds of right hand sides corresponding to receiver locations we demonstrate the high order convergence of our method for several three dimensional targets we prove the high order spectral accuracy of our approximations to the rcs for a class of perfect conductors described globally in spherical coordinates

case deletion diagnostics for mixed models mixed linear models arise in many areas of application standard estimation methods for mixed models are sensitive to bizarre observations such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions we develop case deletion diagnostics for detecting influential observations in mixed linear models diagnostics for both fixed effects and variance components are proposed computational formulas are given that make the procedures feasible the methods are illustrated using examples

a direct approach to false discovery rates summary multiple hypothesis testing involves guarding against much more complicated errors than single hypothesis testing whereas we typically control the type i error rate for a single hypothesis test a compound error rate is controlled for multiple hypothesis tests for example controlling the false discovery rate fdr traditionally involves intricate sequential p value rejection methods based on the observed data whereas a sequential p value method fixes the error rate and estimates its corresponding rejection region we propose the opposite approach we fix the rejection region and then estimate its corresponding error rate this new approach offers increased applicability accuracy and power we apply the methodology to both the positive false discovery rate pfdr and fdr and provide evidence for its benefits it is shown that pfdr is probably the quantity of interest over fdr also discussed is the calculation of the q value the pfdr analogue of the p value which eliminates the need to set the error rate beforehand as is traditionally done some simple numerical examples are presented that show that this new approach can yield an increase of over eight times in power compared with the benjamini hochberg fdr method

a recursive three stage least squares method for large scale systems of simultaneous equations a new numerical method is proposed that uses the qr decomposition and its variants to derive recursively the three stage least squares 3sls estimator of large scale simultaneous equations models sem the 3sls estimator is obtained sequentially once the underlying model is modified by adding or deleting rows of data a new theoretical pseudo sem is developed which has a non positive definite dispersion matrix and is proved to yield the 3sls estimator that would be derived if the modified sem was estimated afresh in addition the computation of the iterative 3sls estimator of the updated observations sem is considered the new recursive method utilizes efficiently previous computations exploits sparsity in the pseudo sem and uses as main computational tool orthogonal and hyperbolic matrix factorizations this allows the estimation of large scale sems which previously could have been considered computationally infeasible to tackle numerical trials have confirmed the effectiveness of the new estimation procedures the new method is illustrated through a macroeconomic application

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

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

high dimensional influence measure influence diagnosis is important since presence of influential observations could lead to distorted analysis and misleading interpretations for high dimensional data it is particularly so as the increased dimensionality and complexity may amplify both the chance of an observation being influential and its potential impact on the analysis in this article we propose a novel high dimensional influence measure for regressions with the number of predictors far exceeding the sample size our proposal can be viewed as a high dimensional counterpart to the classical cook s distance however whereas the cook s distance quantifies the individual observation s influence on the least squares regression coefficient estimate our new diagnosis measure captures the influence on the marginal correlations which in turn exerts serious influence on downstream analysis including coefficient estimation variable selection and screening moreover we establish the asymptotic distribution of the proposed influence measure by letting the predictor dimension go to infinity availability of this asymptotic distribution leads to a principled rule to determine the critical value for influential observation detection both simulations and real data analysis demonstrate usefulness of the new influence diagnosis measure

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

multiple influential point detection in high dimensional regression spaces influence diagnosis should be routinely conducted when one aims to construct a regression model despite its importance the problem of influence quantification is severely under investigated in a high dimensional setting mainly due to the difficulty of establishing a coherent theoretical framework and the lack of easily implementable procedures although some progress has been made in recent years existing approaches are ineffective in detecting multiple influential points especially due to the notorious masking and swamping effects to address this challenge we propose a new group deletion procedure referred to as mip by introducing two novel quantities named max and min statistics these two statistics have complimentary properties in that the max statistic is effective for overcoming the masking effect while the min statistic is useful for overcoming the swamping effect combining their strengths we further propose an efficient algorithm that can detect influential points with prespecified guarantees for wider applications we focus on developing the new proposal for the multiple response regression model encompassing the univariate response linear model as a special case the proposed influential point detection procedure is simple to implement efficient to run and enjoys attractive theoretical properties its effectiveness is verified empirically via extensive simulation study and data analysis

asymptotic properties of bridge estimators in sparse high dimensional regression models we study the asymptotic properties of bridge estimators in sparse high dimensional linear regression models when the number of covariates may increase to infinity with the sample size we are particularly interested in the use of bridge estimators to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero we show that under appropriate conditions bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance thus bridge estimators have an oracle property in the sense of fan and li j amer statist assoc 96 2001 1348 1360 and fan and peng ann statist 32 2004 928 961 in general the oracle property holds only if the number of covariates is smaller than the sample size however under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size