Bounds for the chi-square approximation of Friedman's statistic by Stein's method
利用 Stein 方法界定 Friedman 统计量的卡方近似误差
Friedman's chi-square test is a non-parametric statistical test for $r\geq2$ treatments across $n\ge1$ trials to assess the null hypothesis that there is no treatment effect. We use Stein's method with an exchangeable pair coupling to derive an explicit 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…