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The rate of convergence of some asymptot...
Gaunt, Robert E....

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The rate of convergence of some asymptotically chi-square distributed statistics by Stein's method by Gaunt, Robert E. ( Author )
Lemonjar Open Access
N.A
06-03-2016
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 λ∈R (Pearson's statistic corresponds to λ=1). We obtain a O(n−1) bound for the rate of convergence of Friedman's statistic for any number of treatments r≥2. We also obtain a O(n−1) bound on the rate of convergence of the power divergence statistics for any r≥2 when λ is a positive integer or any real number greater than 5. We conjecture that the O(n−1) rate holds for any λ∈R.
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Article
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36.88 KB
English
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MYR 0.01
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http://arxiv.org/abs/1603.01889
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