The Annals of Statistics
- Ann. Statist.
- Volume 4, Number 4 (1976), 712-722.
A Complete Class Theorem for Strict Monotone Likelihood Ratio With Applications
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.
Ann. Statist., Volume 4, Number 4 (1976), 712-722.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62F10: Point estimation
Secondary: 62F05: Asymptotic properties of tests 62C07: Complete class results 62B05: Sufficient statistics and fields 62H15: Hypothesis testing 62C15: Admissibility
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