Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method

Abstract : We propose a unified study of three statistical settings by widening the ρ-estimation method developed in [BBS17]. More specifically, we aim at estimating a density, a hazard rate (from censored data), and a transition intensity of a time inhomogeneous Markov process. We relate the performance of ρ-estimators to deviations of an empirical process. We deduce non-asymptotic risk bounds for an Hellinger-type loss when the models consist, for instance, of piecewise polynomial functions, multimodal functions, or piecewise convex-concave functions. Under convex-type assumptions on the models, maximum likelihood estimators may coincide with ρ-estimators, and satisfy therefore our risk bounds. However, our results also apply to some models where the maximum likelihood method does not work. Besides, the robustness properties of ρ-estimators are not, in general, shared by maximum likelihood estimators. Subsequently, we present an alternative way, based on estimator selection, to define a piecewise polynomial estimator. We control the risk of the estimator and carry out some numerical simulations to compare our approach with a more classical one based on maximum likelihood only.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01557973
Contributeur : Mathieu Sart <>
Soumis le : jeudi 21 décembre 2017 - 11:23:20
Dernière modification le : jeudi 15 mars 2018 - 10:31:31

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  • HAL Id : hal-01557973, version 2

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Mathieu Sart. Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method. 2017. 〈hal-01557973v2〉

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