A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications
L. D. Brown, Arthur Cohen, W. E. Strawderman
The Annals of Statistics · 1976 · Volume 4 · Issue 4
Abstract
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.
Keywords
62B05, 62C07, 62C15, 62F05, 62F10, 62H15, combined estimators, combined tests, complete class, Confidence sets, estimation, monotone likelihood ratio, monotone procedure, sufficiency, testing
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