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Activity Number: 424
Type: Contributed
Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #307838
Title: Computing Confidence Intervals for Log-Concave Densities
Author(s): Mahdis Azadbakhsh*+ and Hanna Jankowski and Xin Gao
Companies: York University and York University and York University
Keywords: non-parametric density estimation ; log-concave ; maximum likelihood ; confidence interval
Abstract:

In recent years, shape-constraints have been introduced as an effective tool in non-parametric density estimation and the assumption of log-concavity has received particular attention. Balabdaoui et al.(2009) developed pointwise asymptotic theory for the maximum likelihood estimator of the log-concave density. Here, the practical aspects of their result are studied by calculating a pointwise confidence interval for the true log-concave density based on their asymptotic theory. To do this, two quantities need to be approximated: quantiles of the limiting process, and a nuisance parameter which involves the rst and second derivatives of the unknown log-concave density. The obtained confidence interval is studied via simulation.


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