Regularized LRT for Large Scale Covariance Matrices: One Sample Problem

Understand

The main theme of this paper is a modification of the likelihood ratio test (LRT) for testing high dimensional covariance matrix.

• Recently, the correct asymptotic distribution of the LRT for a large-dimensional case (the case $p/n$ approaches to a constant $\gamma \in (0,1]$) is specified by researchers.
• The correct procedure is named as corrected LRT.
• Despite of its correction, the corrected LRT is a function of sample eigenvalues that are suffered from redundant variability from high dimensionality and, subsequently, still does not have full power in differentiating hypotheses on the covariance matrix.