Estimators Based on Data-Driven Generalized Weighted Cramér-von Mises Distances under Censoring – with Applications to Mixture Models

Estimators Based on Data-Driven Generalized Weighted Cramér-von Mises Distances under Censoring – with Applications to Mixture Models

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Article ID: iaor201112546
Volume: 38
Issue: 1
Start Page Number: 108
End Page Number: 129
Publication Date: Mar 2011
Journal: Scandinavian Journal of Statistics
Authors: ,
Keywords: statistics: sampling, simulation: applications
Abstract:

Estimators based on data-driven generalized weighted Cramér-von Mises distances are defined for data that are subject to a possible right censorship. The function used to measure the distance between the data, summarized by the Kaplan–Meier estimator, and the target model is allowed to depend on the sample size and, for example, on the number of censored items. It is shown that the estimators are consistent and asymptotically multivariate normal for every p dimensional parametric family fulfiling 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 sample size dependent and censoring sensitive distance functions for moderate sample sizes. Moreover, the estimators for the mixing proportion seem to be fairly robust against a ‘symmetric’ contamination model even when censoring is present.

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