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Asymptotic formulas for the distributions of the determinant and the trace of a noncentral beta matrix

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  • Fujikoshi, Yasunori

Abstract

Let B be the noncentral beta matrix defined by B = (Sh + Se)-1/2 · Sh(Se + Sh)-1/2, where Se and Sh are independently distributed as Wishart distribution Wp(r, [Sigma]) and noncentral Wishart distribution Wp(q, [Sigma], [Omega]), respectively. Then asymptotic expansions of the distributions of [short parallel] B [short parallel] and Tr B are derived up to order q-3 and q-2 for large q, respectively.

Suggested Citation

  • Fujikoshi, Yasunori, 1972. "Asymptotic formulas for the distributions of the determinant and the trace of a noncentral beta matrix," Journal of Multivariate Analysis, Elsevier, vol. 2(2), pages 208-218, June.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:2:p:208-218
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