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

Christopher S. Withers and Saralees Nadarajah

Statistics & Probability Letters, 2010, vol. 80, issue 23-24, 1954-1961

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.

Keywords: Complex; random; matrices; Edgeworth; expansions; Gaussian (search for similar items in EconPapers)
Date: 2010
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