A new sufficient condition for identifiability of countably infinite mixtures

Lei Yang; Xianyi Wu

doi:10.1007/s00184-013-0444-x

A new sufficient condition for identifiability of countably infinite mixtures

Lei Yang^*
, Xianyi Wu

^*Corresponding author for this work

School of Statistics

East China Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore the identifiability for several distribution families, including normal, gamma, Cauchy, noncentral χ², multivariate normal distributions.

Original language	English
Pages (from-to)	377-387
Number of pages	11
Journal	Metrika
Volume	77
Issue number	3
DOIs	https://doi.org/10.1007/s00184-013-0444-x
State	Published - Apr 2014

Keywords

Countably infinite mixtures
Identifiability
Uniform convergence
Well-ordered set

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abstract = "While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore the identifiability for several distribution families, including normal, gamma, Cauchy, noncentral χ2, multivariate normal distributions.",

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AB - While identifiability of finite mixtures for a wide range of distributions has been studied by statisticians for decades, discussion on countably infinite mixtures is still limited. This article provides an sufficient condition by means of well-ordered sets and uniform convergence of series. It is then applied to revisit some examples for which the identifiability is well established and then explore the identifiability for several distribution families, including normal, gamma, Cauchy, noncentral χ2, multivariate normal distributions.

KW - Countably infinite mixtures

KW - Identifiability

KW - Uniform convergence

KW - Well-ordered set

UR - https://www.scopus.com/pages/publications/84897617803

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DO - 10.1007/s00184-013-0444-x

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JO - Metrika

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A new sufficient condition for identifiability of countably infinite mixtures

Abstract

Keywords

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