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Activity Number: 415
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: SSC
Abstract - #306021
Title: Asymptotics of the Discrete Log-Concave Maximum Likelihood Estimator and Related Applications
Author(s): Hanna Jankowski*+
Companies: York University
Address: Department of Math & Stats, Toronto, ON, M3J 1P3, Canada
Keywords: shape-constraints ; nonparamateric estimation ; log-concave ; confidence interval ; misspecification

The assumption of log-concavity is a flexible and appealing nonparametric shape constraint in distribution modeling. In this work, we study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show that the MLE is strongly consistent and derive its pointwise asymptotic theory under both the well- and misspecifi ed settings. Our asymptotic results are used to calculate con fidence intervals for the true log-concave pmf. The MLE and associated con dence bands may be easily computed using the R package logcondiscr. We illustrate our theoretical results using recent data from the H1N1 pandemic in Ontario, Canada.

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