We show that external randomization may enforce the convergence of test statistics to their limiting distributions in particular cases. This results in a sharper inference. Our approach is based on a central limit theorem for weighted sums. We apply our method to a family of rank-based test statistics and a family of phi-divergence test statistics and prove that, with overwhelming probability with respect to the external randomization, the randomized statistics converge at the rate $O(1/n)$ (up to some logarithmic factors) to the limiting chi-square distribution in Kolmogorov metric.

翻译：我们发现,外部随机化可强制将测试统计数据与特定情况下限制分布的测试统计数据相融合,从而得出更清晰的推论。我们的方法基于加权总和的中央限理论。我们的方法适用于等级测试统计数据的大家庭和两栖体测试统计数据的大家庭,并证明随机化统计数据在外部随机化方面极有可能以1美元/n美元(加上一些对数系数)的汇率集中到科尔莫戈罗夫标准中限制基平方的分布。