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• W2295347816 abstract "We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and establish some simple sufficient conditions for convergence rates of order $n^{-1}$ for smooth test functions. These general bounds are applied to Friedman's statistic for comparing $r$ treatments across $n$ trials and the family of power divergence statistics for goodness-of-fit across $n$ trials and $r$ classifications, with index parameter $lambdainmathbb{R}$ (Pearson's statistic corresponds to $lambda=1$). We obtain a $O(n^{-1})$ bound for the rate of convergence of Friedman's statistic for any number of treatments $rgeq2$. We also obtain a $O(n^{-1})$ bound on the rate of convergence of the power divergence statistics for any $rgeq2$ when $lambda$ is a positive integer or any real number greater than 5. We conjecture that the $O(n^{-1})$ rate holds for any $lambdainmathbb{R}$." @default.
• W2295347816 created "2016-06-24" @default.
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• W2295347816 date "2016-03-06" @default.
• W2295347816 modified "2023-09-27" @default.
• W2295347816 title "The rate of convergence of some asymptotically chi-square distributed statistics by Stein's method" @default.
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