The Annals of Statistics

A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications

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

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343543

Digital Object Identifier
doi:10.1214/aos/1176343543

Mathematical Reviews number (MathSciNet)
MR415821

Zentralblatt MATH identifier
0336.62021

JSTOR
links.jstor.org

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1176343543


Export citation