Berry-Esseen Type Bounds for Transformations of Chi-Squared Variables and Its Statistical Applications

by Ulyanov, Vladimir V.; Christoph, Gerd; Fujikoshi, Yasunori


Preprint series: 06-14, Preprints

The paper is published: Siberian Mathematical Journal, Vol. 47, No. 6, pp. 1154-1166, 2006

62H10 Distribution of statistics
62E20 Asymptotic distribution theory


Abstract: We get computable error bound of order $O(n^{-1})$ for chi-squared with 1 degree of freedom approximation of transformed chi-squared random variable with $n$ degrees of freedom. The result is applied for likelihood ratio statistics in multivariate case.

Keywords: Computable error bound, chi-squared approximation, likelihood ratio statistics, transformation of random variables

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