centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre


Keep in touch

Subscribe to cemmap news

Shape constrained density estimation via penalized Rényi divergence

Authors: Roger Koenker and Ivan Mizera
Date: 18 September 2018
Type: cemmap Working Paper, CWP54/18
DOI: 10.1920/wp.cem.2018.5418


Shape constraints play an increasingly prominent role in nonparametric function estimation. While considerable recent attention has been focused on log concavity as a regularizing device in nonparametric density estimation, weaker forms of concavity constraints encompassing larger classes of densities have received less attention but offer some additional flexibility. Heavier tail behavior and sharper modal peaks are better adapted to such weaker concavity constraints. When paired with appropriate maximal entropy estimation criteria these weaker constraints yield tractable, convex optimization problems that broaden the scope of shape constrained density estimation in a variety of applied subject areas. In contrast to our prior work, Koenker and Mizera (2010), that focused on the log concave (α = 1) and Hellinger (α = 1/2) constraints, here we describe methods enabling imposition of even weaker, α ≤ 0 constraints. An alternative formulation of the concavity constraints for densities in dimension d  2 also signi cantly expands the applicability of our proposed methods for multivariate data. Finally, we illustrate the use of the Renyi divergence criterion for norm-constrained estimation of densities in the absence of a shape constraint.

Download full version

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us