Bounds on Distributions Arising in Order Restricted Inference: The Partially Ordered Case.
Abstract
In testing hypotheses involving order restrictions on a collection of parameters, distributions arise which are mixtures of chi-squared or beta distributions. In general, the mixing coefficients are quite intractable even for a moderate number of populations. Stochastic upper and lower bounds are obtained for mixtures which arise in Bartholomew's tests for homogeneity of normal means with the alternative restricted by a quasi ordering. These bounds are applicable in the dual-testing situation, that is in testing the order restriction as a null hypothesis; in testing order restrictions in exponential families, Poisson intensities and multinomial parameters; and in some nonparametric settings. These can also be applied to obtain the least favorable configuration for testing equality of two multinomial populations with a stochastic ordering alternative. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1985
- Accession Number
- ADA159872
Entities
People
- F. T. Wright