🤖 AI Summary
This study addresses the problem of testing equality of estimable parameters—such as variance, correlation coefficients, and Gini indices—across multiple independent populations using U-statistics. It develops a unified inferential framework that, for the first time, accommodates both fixed-dimensional and increasing-dimensional asymptotic settings within a single approach. The proposed method delivers an asymptotically exact distribution-free inference procedure, combining Wald-type and ANOVA-type statistics with a weighted bootstrap approximation. Theoretical analysis and extensive simulations demonstrate that the method achieves high statistical power and computational efficiency even in finite samples. Its practical utility is further corroborated through real-data applications, confirming its effectiveness in real-world scenarios.
📝 Abstract
This paper proposes a general and unified framework for testing the equality of a broad class of parameters, defined via $U$-statistics, across multiple independent populations. This approach encompasses various common statistical problems, such as comparing variances, correlation coefficients, or Gini indices, among many others. We consider two test statistics, a Wald-type statistic and an ANOVA-type statistic. The asymptotic distribution of the first one is derived under a fixed-dimension regime, whereas the second one is studied under both fixed and increasing-dimension regimes, where the parameter dimension diverges with the sample size. Based on these limiting distributions, we construct test procedures enabling asymptotically exact inference without parametric assumptions. Additionally, an alternative null distribution estimator based on a weighted bootstrap approximation is studied, which is applicable to the ANOVA-type statistic under a fixed-dimension regime. The finite-sample performance and computational efficiency of the proposed procedures are evaluated through an extensive simulation study. Finally, an application to a real dataset illustrates the usefulness of the proposed methodology.