This note re-investigates the smooth tests for the equality of distributions introduced by Bera et al. (2013, Econometric Theory 29, 419–446) and provides a modified smooth test which works for the general case with two sample sizes m and n. Asymptotic properties of the proposed test statistic under both the null and the alternative hypothesis are studied.

中文翻译：

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关于分配均等性的平滑测试

本说明重新研究了 Bera 等人引入的分布相等性的平滑测试。（2013 年，计量经济学理论29, 419–446) 并提供修改后的平滑测试，适用于具有两种样本大小的一般情况米和n. 研究了在零假设和备择假设下提出的检验统计量的渐近特性。