Power Enhancement for Testing the Equality of Shape Matrix Eigenvalues Under Ellipticity

Gaspard Bernard () and Thomas Verdebout ()
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Gaspard Bernard: University of Luxembourg
Thomas Verdebout: Université Libre de Bruxelles

A chapter in Recent Advances in Econometrics and Statistics, 2024, pp 71-86 from Springer

Abstract: Abstract In this work, we consider the problem of testing the null hypotheses ℋ 0 q : λ q , V > λ q + 1 , V = … = λ p , V $$\mathcal {H}_{0q}: \lambda _{q,\mathbf {V}} > \lambda _{q+1,\mathbf {V}}= \ldots = \lambda _{p,\mathbf {V}}$$ where λ 1 , V ≥ … ≥ λ p , V $$\lambda _{1,\mathbf {V}} \geq \ldots \geq \lambda _{p,\mathbf {V}}$$ are the ordered eigenvalues of the shape matrix V $$\mathbf {V}$$ of an elliptical distribution. We propose a class of tests based on signed-rank statistics. Our new tests are constructed (i) to keep the nice properties of the tests introduced in Bernard and Verdebout T (J Multivar Anal, 2023) for the problem, (ii) to improve the detection ability of the same tests in Bernard and Verdebout T (J Multivar Anal, 2023) against alternatives of the form ℋ 1 q : λ q , V = λ q + 1 , V = … = λ p , V $$\mathcal {H}_{1q} : \lambda _{q,\mathbf {V}} = \lambda _{q+1,\mathbf {V}}=\ldots =\lambda _{p,\mathbf {V}}$$ , and (iii) to improve the robustness to outliers and heavy tails in the data-generating process of the pseudo-Gaussian test proposed in Bernard and Verdebout (Stat Sin, 2024). We show through Monte-Carlo simulations that our new tests achieve these objectives.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-61853-6_4

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DOI: 10.1007/978-3-031-61853-6_4

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