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Asymptotics of the discrete log-concave maximum likelihood estimator and related applications


Balabdaoui, Fadoua; Jankowski, Hanna; Rufibach, Kaspar; Pavlides, Marios (2013). Asymptotics of the discrete log-concave maximum likelihood estimator and related applications. Journal of the Royal Statistical Society: Series B, 75(4):769-790.

Abstract

The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log-concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.

Abstract

The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log-concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.

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Citations

8 citations in Web of Science®
10 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:2013
Deposited On:04 Feb 2014 10:35
Last Modified:08 Dec 2017 03:40
Publisher:Wiley-Blackwell
ISSN:1369-7412
Publisher DOI:https://doi.org/10.1111/rssb.12011

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