Statistics Papers

Document Type

Journal Article

Date of this Version

1976

Publication Source

The Annals of Statistics

Volume

4

Issue

4

Start Page

712

Last Page

722

DOI

10.1214/aos/1176343543

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

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

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Date Posted: 27 November 2017

This document has been peer reviewed.