A homogeneity test of large dimensional covariance matrices under non-normality

M. Rauf Ahmad

Kybernetika (2018)

  • Volume: 54, Issue: 5, page 908-920
  • ISSN: 0023-5954

Abstract

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A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as U -statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.

How to cite

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Ahmad, M. Rauf. "A homogeneity test of large dimensional covariance matrices under non-normality." Kybernetika 54.5 (2018): 908-920. <http://eudml.org/doc/294840>.

@article{Ahmad2018,
abstract = {A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as $U$-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.},
author = {Ahmad, M. Rauf},
journal = {Kybernetika},
keywords = {high-dimensional inference; covariance testing; $U$-statistics; non-normality},
language = {eng},
number = {5},
pages = {908-920},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A homogeneity test of large dimensional covariance matrices under non-normality},
url = {http://eudml.org/doc/294840},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Ahmad, M. Rauf
TI - A homogeneity test of large dimensional covariance matrices under non-normality
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 5
SP - 908
EP - 920
AB - A test statistic for homogeneity of two or more covariance matrices is presented when the distributions may be non-normal and the dimension may exceed the sample size. Using the Frobenius norm of the difference of null and alternative hypotheses, the statistic is constructed as a linear combination of consistent, location-invariant, estimators of trace functions that constitute the norm. These estimators are defined as $U$-statistics and the corresponding theory is exploited to derive the normal limit of the statistic under a few mild assumptions as both sample size and dimension grow large. Simulations are used to assess the accuracy of the statistic.
LA - eng
KW - high-dimensional inference; covariance testing; $U$-statistics; non-normality
UR - http://eudml.org/doc/294840
ER -

References

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