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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 969753, 17 pages
http://dx.doi.org/10.1155/2012/969753
Research Article

Testing for Change in Mean of Independent Multivariate Observations with Time Varying Covariance

Institute of Mathematics of Luminy, 163 Avenue de Luminy, 13288 Marseille Cedex 9, France

Received 28 August 2011; Accepted 24 November 2011

Academic Editor: Man Lai Tang

Copyright © 2012 Mohamed Boutahar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a nonparametric CUSUM test for change in the mean of multivariate time series with time varying covariance. We prove that under the null, the test statistic has a Kolmogorov limiting distribution. The asymptotic consistency of the test against a large class of alternatives which contains abrupt, smooth and continuous changes is established. We also perform a simulation study to analyze the size distortion and the power of the proposed test.