-
作者：Bickel, Peter
作者单位：University of California System; University of California Berkeley
-
作者：Rao, N. Raj; Mingo, James A.; Speicher, Roland; Edelman, Alan
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Queens University - Canada; Massachusetts Institute of Technology (MIT)
摘要：We consider settings where the observations are drawn from a zero-mean multivariate (real or complex) normal distribution with the population covariance matrix having eigenvalues of arbitrary multiplicity. We assume that the eigenvectors of the population covariance matrix are unknown and focus on inferential procedures that are based on the sample eigenvalues alone (i.e., eigen-inference). Results found in the literature establish the asymptotic normality of the fluctuation in the trace of po...
-
作者：Radchenko, Peter
作者单位：University of Southern California
摘要：A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from uniform limit theorems for rescaled and reparametrized criterion functions. The new method can handle cases where the standard approach does not yield the complete limiting behavior of the estimator. The asymptotic analysis depends on a decomposition of criteri...
-
作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows dependence between null hypotheses. The dependence can be useful to characterize the spatial structure of the null hypotheses. Asymptotic properties of false discovery proportions and numbers of rejected hypotheses are explored and a large-sample distributional theor...
-
作者：Douc, Randal; Moulines, Eric
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In the last decade, sequential Monte Carlo methods (SMC) emerged as a key tool in computational statistics [see, e.g., Sequential Monte Carlo Methods in Practice (2001) Springer, New York, Monte Carlo Stratergies in Scientific Computing (2001) Springer, New York, Complex Stochastic systems (2001) 109-173]. These algorithms approximate a sequence of distributions by a sequence of weighted empirical measures associated to a weighted population of particles, which are generated recursively. Despi...
-
作者：Zhang, Chunming; Yu, Tao
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Functional magnetic resonance imaging (fMRI) aims to locate activated regions in human brains when specific tasks are performed. The conventional tool for analyzing fMRI data applies some variant of the linear model, which is restrictive in modeling assumptions. To yield more accurate prediction of the time-course behavior of neuronal responses, the semiparametric inference for the underlying hemodynamic response function is developed to identify significantly activated voxels. Under mild regu...
-
作者：Chambaz, Antoine; Rousseau, Judith
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
摘要：The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors are shown to be O(e(-an)) and O((log n)(b) / root n) (a, b > 0), respectively.
-
作者：Zhang, Zhengjun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation coefficient is generally not applicable. One of its most useful features is a test statistic that has high power when testing nonlinear dependence in cases where the Fisher's Z-transformation test may fail to reach a right conclusion. Unlike most asymptotic te...
-
作者：Anderson, Greg W.; Zeitouni, Ofer
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider the spectral properties of a class of regularized estimators of (large) empirical covariance matrices corresponding to stationary (but not necessarily Gaussian) sequences, obtained by banding. We prove a law of large numbers (similar to that proved in the Gaussian case by Bickel and Levina), which implies that the spectrum of a banded empirical covariance matrix is an efficient estimator. Our main result is a central limit theorem in the same regime, which to our knowledge is new, ...
-
作者：Schwartzman, Armin; Mascarenhas, Walter F.; Taylor, Jonathan E.
作者单位：Harvard University; Harvard T.H. Chan School of Public Health; Harvard University; Harvard University Medical Affiliates; Dana-Farber Cancer Institute; Universidade de Sao Paulo; Stanford University
摘要：This article presents maximum likelihood estimators (MLEs) and log-likelihood ratio (LLR) tests for the eigenvalues and eigenvectors of Gaussian random symmetric matrices of arbitrary dimension, where the observations are independent repeated samples from one or two populations. These inference problems are relevant in the analysis of diffusion tensor imaging data and polarized cosmic background radiation data, where the observations are, respectively, 3 x 3 and 2 x 2 symmetric positive defini...
