标题： 测试多个总体中可估计参数的相等性 显示英文标题

标题： Testing the equality of estimable parameters across many populations

摘要： 在$k$人群中的参数比较是统计学中的一个经典问题。 均值或方差相等性的检验是典型的例子。 大多数用于处理这个问题的程序假设$k$是固定的，并且每个人群中都有样本量不断增加的样本。 本文介绍并研究了一种在$k$个人群中对可估计参数进行比较的检验，当$k$很大且每个人群的样本量与$k$相比很小时。 所提出的检验统计量在参数同质性的原假设下渐近分布自由，使得无需参数假设即可进行渐近精确推断。 此外，还研究了该方法在备择假设下的行为。 通过模拟评估其小样本性能，并实施一种线性自助方法以改善在小$k$时的行为。 最后，给出了对一个真实数据集的应用。 显示英文摘要

摘要： The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that samples with increasing sample sizes are available from each population. This paper introduces and studies a test for the comparison of an estimable parameter across $k$ populations, when $k$ is large and the sample sizes from each population are small when compared with $k$. The proposed test statistic is asymptotically distribution-free under the null hypothesis of parameter homogeneity, enabling asymptotically exact inference without parametric assumptions. Additionally, the behaviour of the proposal is studied under alternatives. Simulations are conducted to evaluate its finite-sample performance, and a linear bootstrap method is implemented to improve its behaviour for small $k$. Finally, an application to a real dataset is presented.