Estimators Based on Data-Driven Generalized Weighted Cramer-von Mises Distances Under Censoring, with Applications to Mixture Models

• Activity Number: 463
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Eric Beutner*+
• Companies: Maastricht University
• Keywords: Minimum distance estimation ; Mixture models ; Kaplan-Meier estimator ; Robustness

Abstract

Estimators based on data-driven generalized weighted Cramer-von Mises distances are defined for data that are subject to a possible right censorship. These estimators, in contrast to many minimum distance estimation methods, do neither require approximation methods nor smoothing techniques. This is achieved by replacing integration with respect to a parametric family by integration with respect to a nonparametric estimate. It is shown that the estimators are consistent and asymptotically multivariate normal for every p dimensional parametric family fulfilling some mild regularity conditions. The results are applied to finite mixtures. Simulation results for finite mixtures indicate that the estimators are useful for moderate sample sizes. Furthermore, the simulation results reveal the usefulness of data-driven distance functions for moderate sample sizes and their robustness.