Penalized likelihood density estimation: Cross -validation and some small theories

Jingyuan Wang, Purdue University

Abstract

Penalized likelihood is a very general methodology that can be used in situations where no reasonable parametric model is available. Nonparametric density estimation is a very difficult problem, partially due to the constraints that the estimate must be non-negative and must integrate to 1. Through a logarithm transformation, penalized likelihood provides a very good approach to the problem. The convergence of the estimate to the true density is necessary to justify the usage of this method. The key step in successfully implementing the penalized likelihood method is the smoothing parameter selection. And as a nonparametric method, the estimate is not analytically available, a computation package must be developed to make this tool usable. In this dissertation, a proof is given on convergence in probability; A smoothing parameter selection technique based on cross validation is presented and the empirical performance is studied through simulations; The usage of a computing package written in R is demonstrated.

Degree

Ph.D.

Advisors

Gu, Purdue University.

Subject Area

Statistics

COinS