The Asymptotic Properties of the One-Sample Spatial Rank Methods

: Möttönen, Jyrki; Nordhausen, Klaus; Oja, Hannu; Radojicic, Una

: Barigozzi, Matteo; Hörmann, Siegfried; Paindaveine, Davy

: 1

Publisher: Springer Nature Switzerland

: 2024

: Recent Advances in Econometrics and Statistics: Festschrift in Honour of Marc Hallin

: 49

: 69

: 978-3-031-61852-9

: 978-3-031-61853-6

DOI: https://doi.org/10.1007/978-3-031-61853-6_3(external)

: https://doi.org/10.1007/978-3-031-61853-6_3(external)

For a set of p-variate data points y1, ... yn, 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.

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The work of KN was partly supported by the HiTEc COST Action (CA21163). The work of UR is supported by the Austrian Science Fund (FWF) (5799-N).