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Large and moderate deviation principles for semi-recursive hazard rate kernel estimators defined by stochastic approximation method

Yousri Slaoui

Abstract



In this paper, we prove large and moderate deviation principles for a generalization of the recursive kernel estimators of the hazard rate function defined by the stochastic approximation algorithm introduced by Slaoui [2016. On the choice of smoothing parameters for
semi-recursive nonparametric hazard estimators, J. Stat. Theory Pract, 10 (2016), 656-672]. We show that the estimator constructed using the stepsize which minimizes the variance of the class of the recursive estimators defined in Mokkadem et al. (2009) gives the same pointwise Large Deviations Principles (LDP) and Moderate Deviations Principles (MDP) as the one obtained for the nonrecursive Murthy`s estimator.

Keywords


Hazard rate estimation; Stochastic approximation algorithm; Large and Moderate deviations principles.

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