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. © 2013 Royal Statistical Society.
CITATION STYLE
Balabdaoui, F., Jankowski, H., Rufibach, K., & Pavlides, M. (2013). Asymptotics of the discrete log-concave maximum likelihood estimator and related applications. Journal of the Royal Statistical Society. Series B: Statistical Methodology, 75(4), 769–790. https://doi.org/10.1111/rssb.12011
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