Asymptotics of the discrete log‐concave maximum likelihood estimator and related applications
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.
Document Type: Research Article
Publication date: September 1, 2013