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- W3208952255 abstract "Friedman’s chi-square test is a non-parametric statistical test for r treatments across n trials to assess the null hypothesis that there is no treatment effect. We use Stein’s method with an exchangeable pair coupling to derive a bound on the distance between the distribution of Friedman’s statistic and its limiting chi-square distribution, measured using smooth test functions. Our bound is of the optimal order n−1, and also has an optimal dependence on the parameter r, in that the bound tends to zero if and only if r∕n→0. From this bound, we deduce a Kolmogorov distance bound that decays to zero under the weaker condition r1∕2∕n→0." @default.
- W3208952255 created "2021-11-08" @default.
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- W3208952255 date "2023-08-01" @default.
- W3208952255 modified "2023-09-23" @default.
- W3208952255 title "Bounds for the chi-square approximation of Friedman’s statistic by Stein’s method" @default.
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- W3208952255 doi "https://doi.org/10.3150/22-bej1530" @default.
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