Entropy 2014, 16(7), 4088-4100; doi:10.3390/e16074088
Article

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

1email and 2,* email
Received: 30 April 2014; in revised form: 30 June 2014 / Accepted: 14 July 2014 / Published: 18 July 2014
(This article belongs to the Special Issue Information Geometry)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δn°-1  and that of a transformation Vn-1 of its interior. This transformation is the natural parameter space associated with the family of multinomial distributions. The space Vn-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.
Keywords: simplex; cone; exponential family; monotone likelihood ratio; unimodal; duality
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MDPI and ACS Style

Vos, P.; Anaya-Izquierdo, K. 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 2014, 16, 4088-4100.

AMA Style

Vos P, Anaya-Izquierdo K. 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. 2014; 16(7):4088-4100.

Chicago/Turabian Style

Vos, Paul; Anaya-Izquierdo, Karim. 2014. "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 16, no. 7: 4088-4100.


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