On location mixtures with Pólya frequency components

Fadoua Balabdaoui; Cristina Butucea

doi:10.1016/j.spl.2014.08.013

On location mixtures with Pólya frequency components

Fadoua Balabdaoui
, Cristina Butucea

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

Abstract

We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X₀ with a certain probability. We show that if X₀ admits a density that is a Pólya frequency function with E[X₀]=0, then k, a₁, . . ., a_k and π₁, . . ., π_k are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f₀ when the latter is symmetric.

Original language	English
Pages (from-to)	144-149
Number of pages	6
Journal	Statistics and Probability Letters
Volume	95
DOIs	https://doi.org/10.1016/j.spl.2014.08.013
Publication status	Published - 1 Dec 2014
Externally published	Yes

Keywords

62G10
Identifiability
Laplace transform
Log-concave
Maximum likelihood
Pólya frequency function

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10.1016/j.spl.2014.08.013

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title = "On location mixtures with P{\'o}lya frequency components",

abstract = "We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a P{\'o}lya frequency function with E[X0]=0, then k, a1, . . ., ak and π1, . . ., πk are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f0 when the latter is symmetric.",

keywords = "62G10, Identifiability, Laplace transform, Log-concave, Maximum likelihood, P{\'o}lya frequency function",

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AU - Balabdaoui, Fadoua

AU - Butucea, Cristina

PY - 2014/12/1

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N2 - We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a Pólya frequency function with E[X0]=0, then k, a1, . . ., ak and π1, . . ., πk are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f0 when the latter is symmetric.

AB - We consider the problem of mixing k random variables where each of the k components results from shifting a common random variable X0 with a certain probability. We show that if X0 admits a density that is a Pólya frequency function with E[X0]=0, then k, a1, . . ., ak and π1, . . ., πk are identifiable for any k≥1. We discuss how log-concave maximum likelihood can be used to estimate the mixed and the unknown density f0 when the latter is symmetric.

KW - 62G10

KW - Identifiability

KW - Laplace transform

KW - Log-concave

KW - Maximum likelihood

KW - Pólya frequency function

UR - https://www.scopus.com/pages/publications/84954466580

U2 - 10.1016/j.spl.2014.08.013

DO - 10.1016/j.spl.2014.08.013

M3 - Article

AN - SCOPUS:84954466580

SN - 0167-7152

VL - 95

SP - 144

EP - 149

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

On location mixtures with Pólya frequency components

Abstract

Keywords

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