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What is Learnable in Valiant's Theory of the Learnable? 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The stochastic approximation method for the estimation of a multivariate probability density
Abdelkader Mokkadem, Mariane Pelletier, Yousri Slaoui · 2008-07-18 · via math.ST updates on arXiv.org

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 (1994). We study the properties of these estimators and compare them with Rosenblatt's nonrecursive estimator. It turns out that, for pointwise estimation, it is preferable to use the nonrecursive Rosenblatt's kernel estimator rather than any recursive estimator. A contrario, for estimation by confidence intervals, it is better to use a recursive estimator rather than Rosenblatt's estimator.

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