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Biometrika 1987 74(1):71-83; doi:10.1093/biomet/74.1.71
© 1987 by Biometrika Trust
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Tests for a change-point

BARRY JAMES, KANG LING JAMES and DAVID SIEGMUND

Instituto de Matemática Pura e Aplicada 22460 Rio de Janeiro, Brazil
Department of Statistics, Stanford University Stanford, California 94305, U.S.A.

The problem considered is that of testing a sequence of independent normal random variables with constant, known or unknown, variance for no change in mean versus alternatives with a single change-point. Various tests, such as those based on the likelihood ratio and recursive residuals, are studied. Power approximations are developed by integrating approximations for conditional boundary crossing probabilities. A comparison of several tests is made.

Key Words: Boundary crossing probabilities • Change-point • Likelihood ratio test • Power approximations • Recursive residual


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