Nonparametric Maximum Likelihood Estimation for Mixtures with Partial Priors

• Activity Number: 122
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ji-Ping Wang*+
• Companies: Northwestern University
• Keywords: mixutre models ; nonparametric maximum likelihood estimation

Abstract

Let f(x;G) be a mixture distribution with a known f and an unknown mixing distribution G of an unknown form. We consider estimating a parameter, which can be written as a functional of G, using nonparametric maximum likelihood estimation (NPMLE). However, the plug-in NPML estimator of the parameter can be biased due to a boundary problem that is structurally inherent. We show that a partial prior, defined as a prior distribution of a functional of the mixing distribution, is effective in improving the NPMLE. Computing algorithms and applications in species richness estimation and capture-recapture problems are discussed.