Asymptotic approximations of the inverse moment of the noncentral chi-squared variable. (English) Zbl 1031.62011

Fujioka, Teruo

J. Jpn. Stat. Soc. 31, No. 1, 99-109 (2001).

Summary: The inverse moment of a noncentral chi-squared variable is approximated in simple form based on its asymptotic expansions. The inverse moment is expanded as the noncentrality parameter tends to infinity proportionally to the degrees of freedom. Accuracies of our approximations can be examined through numerical evaluation. It is observed that our approximations perform well in a wide range of values of the noncentrality parameter or degrees of freedom.

MSC:

62E20

Asymptotic distribution theory in statistics

Keywords:

asymptotic expansion; hyergeometric function; James-Stein estimator