Open Access Open Access  Restricted Access Subscription or Fee Access

Multivariate distribution function estimation using stochastic approximation method

Sahar Slama, Yousri Slaoui


In this paper, we generalize the work of Slaoui [2014] to the case of multivariate data. We study the asymptotic properties of this generalized estimators and we compare them with non-recursive Nadaraya’s multivariate distribution estimator. It turns out that, with an adequate choice of the stepsize and an appropriate choice of the bandwidth (h_n), using one of two methods of bandwidth selecti on, the crossvalidation procedure as well as the second generation plug-in method, the MSE (Mean Squared Error) of the generalized estimators can be smaller than the one of Nadaraya estimator. We corroborate our theoretical results through simulations studies and by considering some real datasets.


distribution estimation, multivariate distribution function, stochastic approximation algorithm, smoothing, curve fitting.

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.