Shape Constrained Density Estimation Via Penalized Rényi Divergence

Shape Constrained Density Estimation via Penalized Rényi Divergence

Abstract. 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 beh...

Penalized Bregman Divergence Estimation via Coordinate Descent

Variable selection via penalized estimation is appealing for dimension reduction. For penalized linear regression, Efron, et al. (2004) introduced the LARS algorithm. Recently, the coordinate descent (CD) algorithm was developed by Friedman, et al. (2007) for penalized linear regression and penalized logistic regression and was shown to gain computational superiority. This paper explores...

Shape constrained kernel density estimation

In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modified in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that the resulting estimate is a density itself and shares the asymptotic properties of the unconstrained...

Penalized semiparametric density estimation

In this article we propose a penalized likelihood approach for the semiparametric density model with parametric and nonparametric components. An efficient iterative procedure is proposed for estimation. Approximate generalized maximum likelihood criterion from Bayesian point of view is derived for selecting the smoothing parameter. The finite sample performance of the proposed estimation approa...

Penalized Likelihood Density Estimation :