Asymptotics of the discrete log-concave maximum likelihood estimator and related applications
Fadoua Balabdaoui, Hanna Jankowski, Kaspar Rufibach, Marios Pavlides
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2013 · Volume 75 · Issue 4
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.
Keywords
Confidence interval, Discrete distribution, H1N1, Log-concavity, Misspecification, Non-parametric estimation, Shape constraints
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