A New Adaptive Log-Concave Density Estimator

• Activity Number: 59 - Invited E-Poster Session I
• Type: Invited
• Date/Time: Sunday, August 8, 2021 : 5:45 PM to 6:30 PM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Hanna Jankowski*
• Companies: York University
• Keywords: maximum likelihood; shape constraints; log-concave; adaptive; density

Abstract

One of the great advantages of shape-constrained methods is that they automatically adapt to the underlying level of smoothness in the true density. For example, if the true density has a linear log-density, the MLE of a log concave density will converge at a nearly parametric rate. This is, of course, a great natural advantage of the methodology. In this work we consider modifications to the log-concave maximum likelihood estimator where most original properties are preserved, while the estimator also converges at nearly parametric rates to the Gaussian density.