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

作者：Balabdaoui Fadoua^*; Jankowski Hanna; Rufibach Kaspar; Pavlides Marios

来源：Journal of the Royal Statistical Society - Series B: Statistical Methodology , 2013, 75(4): 769-790.

DOI：10.1111/rssb.12011

• Confidence interval
• Discrete distribution
• H1N1
• Log-concavity
• Misspecification
• Non-parametric estimation
• Shape constraints

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.

• 出版日期2013-9