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Multivariate distribution function estimation using stochastic approximation method

Sahar Slama, Yousri Slaoui

Abstract



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.

Keywords


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

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