87 citations · 248 across the 11 of their papers we have counts for
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Revisiting Révész's stochastic approximation method for the estimation of a regression function
Abdelkader Mokkadem, Mariane Pelletier, Yousri Slaoui
In a pioneer work, Révész (1973) introduces the stochastic approximation method to build up a recursive kernel estimator of the regression function . However, ac…
The stochastic approximation method for the estimation of a multivariate probability density
Abdelkader Mokkadem, Mariane Pelletier, Yousri Slaoui
We apply the stochastic approximation method to construct a large class of recursive kernel estimators of a probability density, including the one introduced by Hall and Patil (199…
Joint behaviour of semirecursive kernel estimators of the location and of the size of the mode of a probability density function
Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam
Let and denote the location and the size of the mode of a probability density. We study the joint convergence rates of semirecursive kernel estimators of and . We sh…
Large and moderate deviations principles for kernel estimators of the multivariate regression
Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam
In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Und…
A companion for the Kiefer--Wolfowitz--Blum stochastic approximation algorithm
Abdelkader Mokkadem, Mariane Pelletier
A stochastic algorithm for the recursive approximation of the location of a maximum of a regression function was introduced by Kiefer and Wolfowitz [Ann. Math. Statist. 23 (195…
Confidence bands for densities, logarithmic point of view
Abdelkader Mokkadem, Mariane Pelletier
Let be a probability density and be an interval on which is bounded away from zero. By establishing the limiting distribution of the uniform error of the kernel estimat…
Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives
Abdelkader Mokkadem, Mariane Pelletier, Baba Thiam
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density…