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The problem of testing the homogeneity of mean directions of several Fisher–von Mises–Langevin (FvML) populations has been studied by several authors under the set up of equal or unequal concentration parameters. In a recent paper, the authors have proposed a heuristic test for testing the homogeneity of mean directions of several FvML populations. They have proposed a nonparametric bootstrap method to compute the critical values of the test. However, the proof of convergence of this nonparametric bootstrap algorithm remains a challenging issue. In this paper, we put forward a detailed proof of the convergence of the nonparametric bootstrap algorithm under the general case of unknown and unequal concentration parameters and unequal sample sizes.

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Asymptotic Accuracy of a Bootstrap Test of Homogeneity in Fisher–von Mises–Langevin Populations

  • 章节

  • 发表日期：

    2025年

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  • Shreyashi Basak,
  • Paavo Sattler,
  • Somesh Kumar

摘要

The problem of testing the homogeneity of mean directions of several Fisher–von Mises–Langevin (FvML) populations has been studied by several authors under the set up of equal or unequal concentration parameters. In a recent paper, the authors have proposed a heuristic test for testing the homogeneity of mean directions of several FvML populations. They have proposed a nonparametric bootstrap method to compute the critical values of the test. However, the proof of convergence of this nonparametric bootstrap algorithm remains a challenging issue. In this paper, we put forward a detailed proof of the convergence of the nonparametric bootstrap algorithm under the general case of unknown and unequal concentration parameters and unequal sample sizes.