Testing for independence of large dimensional vectors

Taras Bodnar, Holger Dette and Nestor Parolya

MPRA Paper from University Library of Munich, Germany

Abstract: In this paper, new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are investigated under the null hypothesis and the alternative hypothesis using random matrix theory. For this purpose, we study the weak convergence of linear spectral statistics of central and (conditionally) noncentral Fisher matrices. In particular, a central limit theorem for linear spectral statistics of large dimensional(conditionally) noncentral Fisher matrices is derived which is then used to analyse the power of the tests under the alternative. The theoretical results are illustrated by means of a simulation study where we also compare the new tests with several alternatives, in particular with the commonly used corrected likelihood ratio test. It is demonstrated that the latter test does not keep its nominal level if the dimension of one sub-vector is relatively small compared to the dimension of the other sub-vector.On the other hand, the tests proposed in this paper provide a reasonable approximation of the nominal level in such situations. Moreover, we observe that one of the proposed tests is most powerful under a variety of correlation scenarios.

Keywords: Testing for independence; large dimensional covariance matrix; noncentral Fisher random matrix; linear spectral statistics; asymptotic normality (search for similar items in EconPapers)
JEL-codes: C12 C18 (search for similar items in EconPapers)
Date: 2019-08-03, Revised 2019-05
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Published in The Annals of Statistics 5.47(2019): pp. 2977-3008

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/97997/1/MPRA_paper_97997.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:97997

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().