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Biometrika 1990 77(2):295-304; doi:10.1093/biomet/77.2.295
© 1990 by Biometrika Trust
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Locating a changed segment in a sequence of Bernoulli variables

YUN-XIN FU and R. N. CURNOW

Department of Applied Statistics, University of Reading Reading RG62AN, U.K.

The theory underlying inferences about a single change point in a sequence of independent Bernoulli variables is extended to the two change points problem where the distance between the two change points is known, namely a changed segment. Both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations. The distribution of the maximum likelihood estimator of the location of the changed segment is derived. Some numerical results for changed segments of length up to 20 are given and computational methods are presented.

Key Words: Bernoulli variable • Change point • Changed segment • Markov chain • Protein structure


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