Open Access Open Access  Restricted Access Subscription or Fee Access

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

Yousri Slaoui


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.