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Article Dans Une Revue Methodology and Computing in Applied Probability Année : 2022

General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters

Résumé

In the present paper, we consider the problem of the estimation of a parameter θ, in Banach spaces, maximizing some criterion function which depends on an unknown nuisance parameter h, possibly infinite-dimensional. The classical estimation methods are mainly based on maximizing the corresponding empirical criterion by substituting the nuisance parameter by a nonparametric estimator. We show that the M-estimators converge weakly to maximizers of Gaussian processes under rather general conditions. The conventional bootstrap method fails in general to consistently estimate the limit law. We show that the m out of n bootstrap, in this extended setting, is weakly consistent under conditions similar to those required for weak convergence of the M-estimators. The aim of this paper is therefore to extend the existing theory on the bootstrap of the M-estimators. Examples of applications from the literature are given to illustrate the generality and the usefulness of our results. Finally, we investigate the performance of the methodology for small samples through a short simulation study.
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Dates et versions

hal-03698865 , version 1 (19-06-2022)

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Salim Bouzebda, Issam Elhattab, Anouar Abdeldjaoued Ferfache. General M-Estimator Processes and their m out of n Bootstrap with Functional Nuisance Parameters. Methodology and Computing in Applied Probability, inPress, ⟨10.1007/s11009-022-09965-y⟩. ⟨hal-03698865⟩
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