## Annals of Statistics

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

### A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications

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

#### 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