Robustness of the likelihood ratio test for detection and estimation of a mean change point in a sequence of elliptically contoured observations

Abstract

The likelihood ratio test (LRT) for testing a mean change after an unknown point in a sequence of n uncorrelated p-dimensional elliptically contoured distributed observations is established. It is shown that the LRT has the same form as well as null distribution as in the multivariate normal case.

Keywords:

• change point
• elliptically contoured distributions
• likelihood-ratio criteria
• invariant
• maximum-likelihood estimators

MSC :

• 62H15
• 62H10
• 62F35

Acknowledgements

The author wishes to thank Professor K. Zografos for his motivation and his valuable comments and suggestions.