Linear shrinkage-based hypothesis test for large-dimensional covariance matrix

Book Chapter (2024)
Author(s)

T. Bodnar (Linkoping University)

N. Parolya (TU Delft - Statistics)

Frederik Veldman (Student TU Delft)

Research Group
Statistics
DOI related publication
https://doi.org/10.1007/978-3-031-69111-9_12
More Info
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Publication Year
2024
Language
English
Research Group
Statistics
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Pages (from-to)
239-257
ISBN (print)
978-3-031-69110-2
ISBN (electronic)
978-3-031-69111-9
Reuse Rights

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Abstract

The chapter is concerned with finding the asymptotic distribution of the estimated shrinkage intensity used in the definition of the linear shrinkage estimator of the covariance matrix, derived by Bodnar et al. (J Multivar Anal 132:215–228, 2014). As a result, a new test statistic is proposed which is deduced from the linear shrinkage estimator. This result is a ready-to-use multivariate hypothesis test in the large-dimensional asymptotic framework and constitutes the main result of the chapter. The theoretical findings are compared by means of a simulation study with existing tests, in particular with the commonly used corrected likelihood ratio test and the corrected John test, both derived by Wang and Yao (Electron J Stat 7:2164–2192, 2013).

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