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Edgeworth expansions for the product of two complex random matrices each with IID components

Author

Listed:
  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

Let and be independent n×n complex matrices with elements i.i.d. as X1+iX2 and Y1+iY2, respectively, where i=(-1)1/2, X1 and X2 are independent and identically distributed, Y1 and Y2 are independent and identically distributed. We obtain Edgeworth expansions for the distribution of any element of (and so for trace ), in Cartesian coordinates. If X1 or Y1 is symmetric about zero, the expansions are given to O(n-4). A specific example applicable to reverberation systems is the case when X1 and Y1 are both Gaussian.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2010. "Edgeworth expansions for the product of two complex random matrices each with IID components," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1954-1961, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1954-1961
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