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The Asymptotic Properties of the One-Sample Spatial Rank Methods

In: Recent Advances in Econometrics and Statistics

Author

Listed:
  • Jyrki Möttönen

    (University of Helsinki, Department of Mathematics and Statistics)

  • Klaus Nordhausen

    (University of Jyväskylä, Department of Mathematics and Statistics)

  • Hannu Oja

    (University of Turku, Department of Mathematics and Statistics)

  • Una Radojicic

    (Vienna University of Technology, Institute of Statistics & Mathematical Methods in Economics)

Abstract

For a set of p-variate data points y 1 , … , y n $$\mathbf y_1,\ldots ,\mathbf y_n$$ , there are several versions of multivariate median and related multivariate sign test proposed and studied in the literature. In this paper we consider the asymptotic properties of the multivariate extension of the Hodges-Lehmann (HL) estimator, the spatial HL-estimator, and the related test statistic. The asymptotic behavior of the spatial HL-estimator and the related test statistic when n tends to infinity are collected, reviewed, and proved, some for the first time though being used already for a longer time. We also derive the limiting behavior of the HL-estimator when both the sample size n and the dimension p tend to infinity.

Suggested Citation

  • Jyrki Möttönen & Klaus Nordhausen & Hannu Oja & Una Radojicic, 2024. "The Asymptotic Properties of the One-Sample Spatial Rank Methods," Springer Books, in: Matteo Barigozzi & Siegfried Hörmann & Davy Paindaveine (ed.), Recent Advances in Econometrics and Statistics, pages 49-69, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61853-6_3
    DOI: 10.1007/978-3-031-61853-6_3
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