J. Japan Statist. Soc., Vol. 31 (No. 1), pp. 99-109, 2001

Asymptotic Approximations of the Inverse Moment of the Noncentral Chi-Squared Variable

Teruo Fujioka

Abstract. The inverse moment of the noncentral chi-squared variable is approximated in simple forms based on its asymptotic expansions. The inverse moment is expanded as the noncentrality parameter tends to infinity proportionally to 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.

Key words and phrases: Asymptotic expansion, Hypergeometric function, James-Stein estimator.

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