Seminar

Estimation of a log-concave probability sequence via maximum likelihood: Asymptotics and related applications

Fadoua Balabdaoui (Université Paris-Dauphine)

March 25, 2014, 14:00–15:30

Toulouse

Room MF 323

Statistics Seminar

Abstract

Log-concavity is a flexible and appealing modeling assumption which has been widely used in nonparametric density estimation. In this work, we extend this model to the discrete setting and study the log-concave maximum likelihood estimator (MLE) of a probability mass function (pmf). We show that the MLE is strongly consistent and establish its pointwise asymptotic theory under both the well- and misspecified settings. The obtained asymptotic results are used to compute confidence intervals for the unknown pmf. We illustrate our theoretical results using recent data from the H1N1 pandemic in Ontario, Canada.