67 citations · 161 across the 9 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…