The Heavy Tailed Inverse Convex Shape Constraint

• Activity Number: 505
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Clifford Anderson-Bergman*+
• Companies: University of California, Irvine
• Keywords: Shape Constraints ; Inverse-Convex ; Log-Concave ; Non-parametric ; Density Estimation

Abstract

The log-concave shape constrained density estimator has received much attention in recent years, providing consistent density estimation without the need to select a parametric distribution or smoothing parameters. However, for heavy tailed data, the log-concave assumption may be inappropriate, as it allows only up to exponential tails. To address this concern, we present a new shape constraint we call inverse convex. We show that the family of log-concave distributions fits properly into the family of inverse convex and that inverse convex also allows for heavier tails. We present other basic properties of the family of inverse convex distributions, interesting characteristics of the inverse convex estimator (including an unbounded likelihood function), and apply the new estimator to fit income data.