×

zbMATH — the first resource for mathematics

Computable error bounds for asymptotic expansions of the hypergeometric function \({}_1F_1\) of matrix argument and their applications. (English) Zbl 1116.62026
Summary: We derive error bounds for asymptotic expansions of the hypergeometric functions \({}_1F_1(n; n+b; Z)\) and \({}_1F_1(n; n+b; -Z)\), where \(Z\) is a \(p \times p\) symmetric nonnegative definite matrix. The first result is applied for theoretical accuracy of approximating the moments of \(\Lambda=|S_e|/|S_e+S_h|\), where \(S_h\) and \(S_e\) are independently distributed as a noncentral Wishart distribution \(W_p(q, \Sigma, \Sigma^{1/2} \Omega \Sigma^{1/2})\) and a central Wishart distribution \(W_p(n, \Sigma)\), respectively. The second result is applied for theoretical accuracy of approximating the probability density function of the maximum likelihood estimators of regression coefficients in the growth curve model.
MSC:
62E20 Asymptotic distribution theory in statistics
62H10 Multivariate distribution of statistics
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
33C90 Applications of hypergeometric functions
PDF BibTeX XML Cite
Full Text: Euclid