Penalized Likelihood-Tuned Density Estimator

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yeojin Chung*+ and Bruce G. Lindsay
• Companies: Penn State and Penn State
• Keywords: density estimation ; nonparametric mixture ; nonparametric likelihood ; penalized likelihood

Abstract

We consider an improved multivariate nonparametric density estimator which arises from treating the kernel density estimator as an element of the model that consists of all mixtures of the kernel, continuous or discrete. One can obtain the kernel density estimator with "likelihood-tuning" by using the uniform density as the starting value in an EM algorithm. The second tuning leads to a fitted density with higher likelihood than the kernel density estimator. A penalized version of the likelihood-tuning gives the kernel density estimator with t-kernel with the first tuning. The second penalized-tuning leads to a density estimator with local shape adaptation in t-kernel function. We compare the performance of the new density estimators with and without penalization.