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

Entropy

Paul Vos¹ 

[1] Department of Biostatistics, East Carolina University, Greenville, NC 27858, USA; E-Mail:

关键词: simplex;    cone;    exponential family;    monotone likelihood ratio;    unimodal;    duality;   

DOI  :  10.3390/e16074088

来源: mdpi

【 摘 要 】

One dimensional exponential families on finite sample spaces are studied using the geometry of the simplexand that of a transformation V_n−1 of its interior. This transformation is the natural parameter space associated with the family of multinomial distributions. The space V_n−1 is partitioned into cones that are used to find one dimensional families with desirable properties for modeling and inference. These properties include the availability of uniformly most powerful tests and estimators that exhibit optimal properties in terms of variability and unbiasedness.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland