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退化 U 统计量广义自助法的一致性AI 解读

A generalized bootstrap version is defined for degenerate $U$-statistics. Our main result shows that the (conditional) distribution function of the bootstrapped degenerate $U$-statistic provides a consistent estimator for the unknown distribution function of the degenerate $U$-statistic under consideration. For the proof we rely on a rank statistic approach.

原假设与备择下简单线性秩统计量的收敛速度AI 解读

Convergence rates for distributions of simple linear rank statistics are investigated. Both the null hypothesis and near alternatives are considered. The method of proof consists in approximating the characteristic function of the statistic by that of a sum of independent random variables and then applying standard tools.