Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications
Fujikoshi, Yasunori
Hiroshima Math. J., Tome 37 (2007) no. 1, p. 13-23 / Harvested from Project Euclid
In this paper 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.
Publié le : 2007-03-14
Classification:  Applications,  asymptotic expansions,  error bounds,  ${}_1F_1$,  hypergeometric functions,  matrix argument,  62H10,  62E20
@article{1176324092,
     author = {Fujikoshi, Yasunori},
     title = {Computable error bounds for asymptotic expansions of the hypergeometric function ${}\_1F\_1$ of matrix argument and their applications},
     journal = {Hiroshima Math. J.},
     volume = {37},
     number = {1},
     year = {2007},
     pages = { 13-23},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176324092}
}
Fujikoshi, Yasunori. Computable error bounds for asymptotic expansions of the hypergeometric function ${}_1F_1$ of matrix argument and their applications. Hiroshima Math. J., Tome 37 (2007) no. 1, pp.  13-23. http://gdmltest.u-ga.fr/item/1176324092/