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Estimators based on data-driven generalized weighted Cramér-von Mises distances under censoring – with applications to mixture models. (English) Zbl 1246.62080
Summary: 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.

MSC:
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62N01 Censored data models
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)
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