Annals of Statistics

A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications

L. D. Brown, Arthur Cohen, and W. E. Strawderman

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Suppose a random variable has a density belonging to a one parameter family which has strict monotone likelihood ratio. For inference regarding the parameter (or a monotone function of the parameter) consider the loss function to be bowl shaped for each fixed parameter and also to have each action be a "point of increase" or a "point of decrease" for some value of the parameter. Under these conditions, given any nonmonotone decision procedure, a unique monotone procedure is constructed which is strictly better than the given procedure for all the above loss functions. This result has application to the following areas: combining data problems, sufficiency, a multivariate one-sided testing problem.

Article information

Ann. Statist., Volume 4, Number 4 (1976), 712-722.

First available in Project Euclid: 12 April 2007

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Primary: 62F10: Point estimation
Secondary: 62F05: Asymptotic properties of tests 62C07: Complete class results 62B05: Sufficient statistics and fields 62H15: Hypothesis testing 62C15: Admissibility

Monotone likelihood ratio complete class monotone procedure sufficiency testing estimation confidence sets combined tests combined estimators


Brown, L. D.; Cohen, Arthur; Strawderman, W. E. A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications. Ann. Statist. 4 (1976), no. 4, 712--722. doi:10.1214/aos/1176343543.

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