Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria

A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation

We propose a class of penalized nonparametric maximum likelihood estimators (NPMLEs) for the species richness problem. We use a penalty term on the likelihood because likelihood estimators that lack it have an extreme instability problem. The estimators are constructed using a conditional likelihood that is simpler than the full likelihood. We show that the full-likelihood NPMLE solution given ...

Penalized Likelihood Density Estimation :

Nonparametric Density Estimation: A Piecewise Maximum Likelihood Approach

The effort of recovering the features (such as the number of modes and overall shape) of unknown densities leads to nonparametric curve estimation under order restrictions. We introduce a flexible class of nonparametric densities called a-regular shaped densities, and propose the Piecewise Maximum Likelihood Estimate (PMLE) which has an attractive "automatic" bandwidth selection feature. Spline...

Maximum likelihood estimation using probability density functions of order statistics

0360-8352/$ see front matter Published by Elsevier doi:10.1016/j.cie.2010.01.008 q This manuscript was processed by Area Editor E.A * Tel.: +1 845 938 5988. E-mail address: [email protected] A variation of maximum likelihood estimation (MLE) of parameters that uses probability density functions of order statistic is presented. Results of this method are compared with traditional maximum like...

Conditional Density Estimation by Penalized Likelihood Model Selection and Applications

In this technical report, we consider conditional density estimation with a maximum likelihood approach. Under weak assumptions, we obtain a theoretical bound for a KullbackLeibler type loss for a single model maximum likelihood estimate. We use a penalized model selection technique to select a best model within a collection. We give a general condition on penalty choice that leads to oracle ty...