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Biometrika 1990 77(2):411-414; doi:10.1093/biomet/77.2.411
© 1990 by Biometrika Trust
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MISCELLANEA

Asymptotic distributions of maximum likelihood tests for change in the mean

EDIT GOMBAY and LAJOS HORVATH

Department of Statistics and Applied Probability, University of Alberta, Edmonton Alberta T6G 2G1, Canada
Department of Mathematics, University of Utah Salt Lake City, Utah 84112, U.S.A.

For the maximum likelihood tests for a change in the mean of independent random variables, it is proved that the limit distribution is a double exponential, i.e. Gumbel, distribution. Our results also explain why the maximum likelihood methods are very powerful on the tails.

Key Words: Brownianbridge • Change-point • Gumbel distribution • Limittheorems • Ornstein-Uhlenbeck process


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