
On the power of axial tests of uniformity on spheres
Testing uniformity on the pdimensional unit sphere is arguably the most...
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Testing Hypotheses about Covariance Matrices in General MANOVA Designs
We introduce a unified approach to testing a variety of rather general n...
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Likelihood Ratio Test in Multivariate Linear Regression: from Low to High Dimension
Multivariate linear regressions are widely used statistical tools in man...
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Analysis on the Empirical Spectral Distribution of Large Sample Covariance Matrix and Applications for Large Antenna Array Processing
This paper addresses the asymptotic behavior of a particular type of inf...
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Fisher's combined probability test for highdimensional covariance matrices
Testing large covariance matrices is of fundamental importance in statis...
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A NeighborhoodAssisted Hotelling's T^2 Test for HighDimensional Means
This paper aims to revive the classical Hotelling's T^2 test in the "lar...
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Setbased differential covariance testing for highthroughput data
The problem of detecting changes in covariance for a single pair of feat...
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A general method for power analysis in testing high dimensional covariance matrices
Covariance matrix testing for high dimensional data is a fundamental problem. A large class of covariance test statistics based on certain averaged spectral statistics of the sample covariance matrix are known to obey central limit theorems under the null. However, precise understanding for the power behavior of the corresponding tests under general alternatives remains largely unknown. This paper develops a general method for analyzing the power behavior of covariance test statistics via accurate nonasymptotic power expansions. We specialize our general method to two prototypical settings of testing identity and sphericity, and derive sharp power expansion for a number of widely used tests, including the likelihood ratio tests, LedoitNagaoWolf's test, CaiMa's test and John's test. The power expansion for each of those tests holds uniformly over all possible alternatives under mild growth conditions on the dimensiontosample ratio. Interestingly, although some of those tests are previously known to share the same limiting power behavior under spiked covariance alternatives with a fixed number of spikes, our new power characterizations indicate that such equivalence fails when many spikes exist. The proofs of our results combine techniques from Poincarétype inequalities, random matrices and zonal polynomials.
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