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Biometrika 1994 81(3):595-601; doi:10.1093/biomet/81.3.595
© 1994 by Biometrika Trust
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MISCELLANEA

Power of the scan statistic in detecting a changed segment in a Bernoulli sequence

SYLVAN WALLENSTEIN1, JOSEPH NAUS2 and JOSEPH GLAZ3

1 Department of Biomathematics, Mount Sinai School of Medicine Box 1023, 1 Gustave Levy Place, New York, New York 10029, U.S.A.
2 Department of Statistics, Rutgers University New Brunswick, New Jersey 08903, U.S.A.
3 Department of Statistics, University of Connecticut Storrs, Connecticut 06269–3120, U.S.A.

Received for publication 1 August 1993. Revision received 1 October 1993.
  Abstract

Fu & Curnow (1990) derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length, based on the scan statistic, the maximum number of successes within the specified length. Their method is computationally feasible for segment lengths of 20 or less. We present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths. We also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length.

Key Words: Bernoulli variable • Change-point • DNA sequence • Matching • Scan statistic


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