
CLT for LSS of sample covariance matrices with unbounded dispersions
Under the highdimensional setting that data dimension and sample size t...
read it

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...
read it

Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
In this paper, we consider the separable covariance model, which plays a...
read it

Discrete convolution statistic for hypothesis testing
The question of testing for equality in distribution between two linear ...
read it

An urn model with local reinforcement: a theoretical framework for a chisquared goodness of fit test with a big sample
Motivated by recent studies of big samples, this work aims at constructi...
read it

Spiked separable covariance matrices and principal components
We introduce a class of separable sample covariance matrices of the form...
read it

Towards a unified theory for testing statistical hypothesis: Multinormal mean with nuisance covariance matrix
Under a multinormal distribution with arbitrary unknown covariance matri...
read it
Central Limit Theory for Linear Spectral Statistics of Normalized Separable Sample Covariance Matrix
This paper focuses on the separable covariance matrix when the dimension p and the sample size n grow to infinity but the ratio p/n tends to zero. The separable sample covariance matrix can be written as n^1A^1/2XBX^⊤ A^1/2, where A and B correspond to the crossrow and crosscolumn correlations, respectively. We normalize the separable sample covariance matrix and prove the central limit theorem for corresponding linear spectral statistics, with explicit formulas for the mean and covariance function. We apply the results to testing the correlations of a large number of variables with two common examples, related to spatialtemporal model and matrixvariate model, which are beyond the scenarios considered in existing studies. The asymptotic sizes and powers are studied under mild conditions. The computations of the asymptotic mean and variance are involved under the null hypothesis where A is the identity matrix, with simplified expressions which facilitate to practical usefulness. Extensive numerical studies show that the proposed testing statistic performs sufficiently reliably under both the null and alternative hypothesis, while a conventional competitor fails to control empirical sizes.
READ FULL TEXT
Comments
There are no comments yet.