Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2017

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

Mathieu Sart
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Résumé

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 a (possibly unbounded) empirical process. We deduce non-asymptotic risk bounds for an Hellinger-type loss on possibly random models. When the models are convex, maximum likelihood estimators 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 procedure to ρ-estimation, more numerically friendly, that yields a piecewise polynomial estimator. We prove theoretical results and carry out some numerical simulations that show the benefits of our approach compared with a more classical one based on maximum likelihood.
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Dates et versions

hal-01557973 , version 1 (06-07-2017)
hal-01557973 , version 2 (21-12-2017)
hal-01557973 , version 3 (31-01-2018)
hal-01557973 , version 4 (07-11-2018)
hal-01557973 , version 5 (22-07-2020)

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  • HAL Id : hal-01557973 , version 1

Citer

Mathieu Sart. Estimating a density, a hazard rate, and a transition intensity via the ρ-estimation method. 2017. ⟨hal-01557973v1⟩
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