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

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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.
Original languageEnglish
Pages (from-to)4088-4100
JournalEntropy
Volume16
Issue number7
DOIs
Publication statusPublished - 18 Jul 2014

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likelihood ratio
tendencies
geometry
inference
estimators
availability
cones

Keywords

  • Simplex
  • cone
  • exponential family
  • monotone-likelihood-ratio
  • unimodal
  • duality

Cite this

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title = "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",
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",
author = "Paul Vos and {Anaya Izquierdo}, {K A}",
year = "2014",
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doi = "10.3390/e16074088",
language = "English",
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pages = "4088--4100",
journal = "Entropy",
issn = "1099-4300",
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AU - Vos, Paul

AU - Anaya Izquierdo, K A

PY - 2014/7/18

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N2 - 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.

AB - 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.

KW - Simplex

KW - cone

KW - exponential family

KW - monotone-likelihood-ratio

KW - unimodal

KW - duality

UR - http://dx.doi.org/10.3390/e16074088

UR - http://www.mdpi.com/1099-4300/16/7/4088

U2 - 10.3390/e16074088

DO - 10.3390/e16074088

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EP - 4100

JO - Entropy

JF - Entropy

SN - 1099-4300

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ER -