Asymptotic expansions for distributions of latent roots in multivariate analysis

A. G. Constantine and R. J. Muirhead

Journal of Multivariate Analysis, 1976, vol. 6, issue 3, 369-391

Abstract: Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)-1, where S1 is Wm(n1, [Sigma], [Omega]) and S2 is Wm(n2, [Sigma]), is studied in detail and asymptotic series for the distribution are obtained which are valid for some or all of the roots of the noncentrality matrix [Omega] large. These expansions are obtained using partial-differential equations satisfied by the distribution. Asymptotic series are also obtained for the distributions of the roots of n-1S, where S in Wm(n, [Sigma]), for large n, and S1S2-1, where S1 is Wm(n1, [Sigma]) and S2 is Wm(n2, [Sigma]), for large n1 + n2.

Keywords: Asymptotic; distributions; latent; roots; asymptotic; expansions; partial-differential; equations (search for similar items in EconPapers)
Date: 1976
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Citations: View citations in EconPapers (6)

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