Likelihood Ratio Tests for a Change in the Multivariate Normal Mean
作者:
M.S. Srivastava,
K.J. Worsley,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1986)
卷期:
Volume 81,
issue 393
页码: 199-204
ISSN:0162-1459
年代: 1986
DOI:10.1080/01621459.1986.10478260
出版商: Taylor & Francis Group
关键词: Change point;Binary segmentation;Bonferroni inequality;Extramultinomial variation
数据来源: Taylor
摘要:
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 HotellingT2for the sequences before and after the change point. 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. 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 Chernoff (1973) by the “faces” method and to find changes in the frequencies of pronouns in the plays of Shakespeare.
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