Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Measure of Central Tendency

We consider m independent one parameter exponential families with parameters (θ1, θ2, , θ m), and the alternative hypothesis [Formula: see text] where [Formula: see text] are specified. The null hypothesis Ho 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

Download Full-text

Uniformly Most Accurate Upper Tolerance Limits for Monotone Likelihood Ratio Families of Discrete Distributions

Journal of the American Statistical Association ◽

10.1080/01621459.1970.10481081 ◽

1970 ◽

Vol 65 (329) ◽

pp. 307-316 ◽

Cited By ~ 14

Author(s):

S. Zacks

Keyword(s):

Likelihood Ratio ◽

Discrete Distributions ◽

Tolerance Limits ◽

Monotone Likelihood Ratio

Download Full-text

A conditional likelihood ratio test for order restrictions in exponential families

Mathematical Social Sciences ◽

10.1016/0165-4896(87)90018-7 ◽

1987 ◽

Vol 14 (2) ◽

pp. 141-159 ◽

Cited By ~ 8

Author(s):

Geoffrey J. Iverson ◽

Steven Alex Harp

Keyword(s):

Likelihood Ratio ◽

Likelihood Ratio Test ◽

Exponential Families ◽

Ratio Test ◽

Conditional Likelihood ◽

Order Restrictions

Download Full-text

Multivariate monotone likelihood ratio and uniform conditional stochastic order

Journal of Applied Probability ◽

10.2307/3213530 ◽

1982 ◽

Vol 19 (3) ◽

pp. 695-701 ◽

Cited By ~ 43

Author(s):

Ward Whitt

Keyword(s):

Conditional Probability ◽

Likelihood Ratio ◽

Probability Distributions ◽

Stochastic Order ◽

Total Positivity ◽

Probability Measures ◽

Monotone Likelihood Ratio ◽

Fkg Inequality ◽

The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn. Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

Download Full-text