The Asymptotic Properties of the One-Sample Spatial Rank Methods

Jyrki Möttönen (), Klaus Nordhausen (), Hannu Oja () and Una Radojicic ()
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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

A chapter in Recent Advances in Econometrics and Statistics, 2024, pp 49-69 from Springer

Abstract: 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.

Keywords: Spatial HL-estimator; Spatial median; Spatial signed-rank test (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61853-6_3

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DOI: 10.1007/978-3-031-61853-6_3

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