Maximum likelihood estimation and confidence bands for a discrete log-concave distribution

Details Maximum likelihood estimation and confidence bands for a discrete log-concave distribution Maximum likelihood estimation and confidence bands for a discrete log-concave distribution

2011-07-20

arxiv.org/abs/1107.3904v1

Statistics

Methodology

41 pages, 8 Figures

Scientific paper

The assumption of log-concavity is an attractive and flexible nonparametric shape constraint in distribution modelling. In this work, we study the maximum likelihood estimator (MLE) of a log-concave probability mass function. We show that the MLE is strongly consistent and derive pointwise asymptotic theory, which is used to calculate confidence bands for the true probability mass function. The proposed estimator and associated confidence bands may be easily computed using the R package logcondiscr. We illustrate the flexibility of the estimator on recent data from the H1N1 pandemic in Ontario, Canada.

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