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Optimal hypothesis testing for high dimensional covaraiance matrices
 Bernoulli
, 2013
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Central Limit Theorems for Classical Likelihood Ratio Tests for HighDimensional Normal Distributions
"... For random samples of size n obtained from pvariate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the highdimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting d ..."
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Cited by 10 (3 self)
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For random samples of size n obtained from pvariate normal distributions, we consider the classical likelihood ratio tests (LRT) for their means and covariance matrices in the highdimensional setting. These test statistics have been extensively studied in multivariate analysis and their limiting distributions under the null hypothesis were proved to be chisquare distributions as n goes to infinity and p remains fixed. In this paper, we consider the highdimensional case where both p and n go to infinity with p/n → y ∈ (0, 1]. We prove that the likelihood ratio test statistics under this assumption will converge in distribution to normal distributions with explicit means and variances. We perform the simulation study to show that the likelihood ratio tests using our central limit theorems outperform those using the traditional chisquare approximations for analyzing highdimensional data.
Supplement to “Universal asymptotics for highdimensional sign tests
, 2013
"... In a smalln largep hypothesis testing framework, most procedures in the literature require quite stringent distributional assumptions, and restrict to a specific scheme of (n, p)asymptotics. More precisely, multinormality is almost always assumed, and it is imposed, typically, that p/n → c, fo ..."
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Cited by 5 (3 self)
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In a smalln largep hypothesis testing framework, most procedures in the literature require quite stringent distributional assumptions, and restrict to a specific scheme of (n, p)asymptotics. More precisely, multinormality is almost always assumed, and it is imposed, typically, that p/n → c, for some c in some given convex set C ⊂ (0,∞). Such restrictions clearly jeopardize practical relevance of these procedures. In this paper, we consider several classical testing problems in multivariate analysis, directional statistics, and multivariate time series: the problem of testing uniformity on the unit sphere, the spherical location problem, the problem of testing that a process is white noise versus serial dependence, the problem of testing for multivariate independence, and the problem of testing for sphericity. In each case, we show that the natural sign tests enjoy nonparametric validity and are distributionfree in a “universal ” (n, p)asymptotics framework, where p may go to infinity in an arbitrary way as n does. Simulations confirm our asymptotic results. 1. Introduction. There
RAPTT: An Exact TwoSample Test in High Dimensions Using Random Projections. ArXiv eprints
, 1405
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HighDimensional Tests for Spherical Location and Spiked Covariance
"... Highdimensional tests for spherical location and spiked covariance ..."
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Highdimensional tests for spherical location and spiked covariance
A Global Homogeneity Test for HighDimensional Linear Regression
, 2013
"... Abstract: This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from estimation uncertainties. Adopting a neighborhood approach, ..."
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Abstract: This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from estimation uncertainties. Adopting a neighborhood approach, we consider a twosample linear regression model with random design and propose a procedure to test whether these two regressions are the same. Relying on multiple testing and variable selection strategies, we develop a testing procedure that applies to highdimensional settings where the number of covariates p is larger than the number of observations n1 and n2 of the two samples. Both type I and type II errors are explicitely controlled from a nonasymptotic perspective and the test is proved to be minimax adaptive to the sparsity. The performances of the test are evaluated on simulated data. Moreover, we illustrate how this procedure can be used to compare genetic networks on Hess et al breast cancer microarray dataset.