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Zbl 0589.62037
Srivastava, M.S.; Worsley, K.J.
Likelihood ratio tests for a change in the multivariate normal mean. (English)
[J] J. Am. Stat. Assoc. 81, 199-204 (1986). ISSN 0162-1459; ISSN 1537-274X/e

Summary: A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling $T\sp 2$ for the sequences before and after the change point. \par The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality. If the change is judged significant, then further changes are estimated by splitting the two subsequences formed by the first change point. \par The methods can also be used to test for a change in row probabilities of a contingency table, allowing for extramultinomial variation. The results are used to find changes in a set of geological data previously analyzed by {\it H. Chernoff} [The use of faces to represent points in k- dimensional space graphically. ibid. 68, 361-368 (1973)] by the "faces" method and to find changes in the frequencies of pronouns in the plays of Shakespeare.

MSC 2000:: *62H15 Multivariate hypothesis testing
62E20 Asymptotic distribution theory in statistics

Keywords: binary segmentation; change in mean; maximum Hotelling T-square; independent multivariate normal vectors; likelihood ratio test; change point; improved Bonferroni inequality; change in row probabilities of a contingency table; extramultinomial variation; geological data

Cited in: Zbl 0822.62048

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