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

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