Improved Tests for an Ordered Hypothesis in one Parameter Exponential Families

Abstract

We consider m independent one parameter exponential families with parameters (θ₁, θ₂,  , θ _m ), and the alternative hypothesis $H_1:{\theta }_4>{\theta }_i^0,i=1,2,\dots ,m,$ where ${\theta }_i^0\text{'}\text{s}$ are specified. The null hypothesis H_o is the complement of H₁. A class of tests more powerful than the likelihood ratio test (LRT) is derived. Applications to two special cases, Binomial and Poisson, are indicated.

AMS 1980 Subject Classification: Primary 62F03