Testing the equality of estimable parameters

M. Romero Madroñal, M. R. Sillero Denamiel, M. D. Jiménez Gamero

In this talk, we propose a general, unified framework for testing the equality of a broad class of estimable parameters, defined via U-statistics, across multiple independent populations. This framework encompasses various common statistical problems, such as comparing variances, correlation coefficients, and Gini indices. We consider two test statistics: a Wald-type and an ANOVA-type. While the asymptotic distribution of the former is derived under a fixed-dimension regime, the latter is analyzed in both fixed and high-dimensional settings, where the parameter dimension is permitted to grow with the sample size. These results yield testing procedures that enable asymptotically exact inference without parametric assumptions. We also discuss an alternative approach to approximating the null distribution based on a weighted bootstrap. The performance of the proposed procedures is illustrated through simulations, and their practical utility is shown via an application to a real dataset.

Keywords: Multivariate inference, Non-parametric testing, U-statistics, Increasing dimension

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