Appendix to Detection of weak signals in high-dimensional complex-valued data

@inproceedings{Onatski2012AppendixTD,
title={Appendix to Detection of weak signals in high-dimensional complex-valued data},
author={Alexei Onatski},
year={2012}
}

Alexei Onatski

Published 2012

This note contains an elementary proof of Corollary 1, a proof of formula (24), and a derivation of the asymptotic power of some previously proposed tests of sphericity and equality of the covariance matrix to the identity matrix. A Elementary proof of Corollary 1. Let ~ A = diag (~ a1; :::; ~ ap) and ~ B = diag ~b1; :::;~bp be such that ~ a1 > ::: > ~ ap > 0 and ~b1 > ::: > ~bp > 0: The right-hand side of (12)1 is understood as lim ~ A!A; ~ B!B Qp 1 k=1 k! Vp ~ A Vp ~ B det 1 i;j p e ai ~bj… CONTINUE READING