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Sugiura, Nariaki

Asymptotic solutions of the hypergeometric function \(_1F_1\) of matrix argument, useful in multivariate analysis. (English) Zbl 0314.62023

Ann. Inst. Stat. Math. 24, 517-524 (1972).
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Cited in 4 Documents

MSC:

62H10 Multivariate distribution of statistics
62H15 Hypothesis testing in multivariate analysis
35A35 Theoretical approximation in context of PDEs
33C05 Classical hypergeometric functions, \({}_2F_1\)
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References:

[1] Constantine, A. G. (1963). Some non-central distribution problems in multivariate analysis,Ann. Math. Statist.,34, 1270–1285. · Zbl 0123.36801 · doi:10.1214/aoms/1177703863
[2] Fujikoshi, Y. (1968). Asymptotic expansion of the distribution of the generalized variance in the non-central case,J. Sci. Hiroshima Univ, Ser. A-I,32, 293–299. · Zbl 0246.62065
[3] Muirhead, R. J. (1970). Systems of partial differential equations for hypergeometric functions of matrix argument.Ann. Math. Statist.,41, 991–1001. · Zbl 0225.62078 · doi:10.1214/aoms/1177696975
[4] Muirhead, R. J. (1970). Asymptotic distributions of some multivariate tests,Ann. Math. Statist.,41, 1002–1010. · Zbl 0214.46506 · doi:10.1214/aoms/1177696976
[5] Nagao, H. (1970). Asymptotic expansions of some test criteria for homogeneity of variances and covariance matrices from normal populations,J. Sci. Hiroshima Univ., Ser. A-I,34, 153–247. · Zbl 0228.62016
[6] Sugiura, N. (1971). Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis, Submitted toAnn. Inst. Statist. Math. · Zbl 0338.62027
[7] Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence.Ann. Math. Statist.,40, 942–952. · Zbl 0184.22303 · doi:10.1214/aoms/1177697599
[8] Sugiura, N. and Nagao, H. (1971). Asymptotic expansion of the distribution of the generalized variance for noncentral Wishart matrix, when {\(\Omega\)}=0(n),Ann. Inst. Statist. Math.,23, 469–475. · Zbl 0255.62016 · doi:10.1007/BF02479244
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