Large and moderate deviation principles for recursive kernel density estimators defined by stochastic approximation method

In this paper we prove large and moderate deviations principles for the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm introduced by Mokkadem et al. [2009. The stochastic approximation method for the estimation of a probability density. J. Statist. Plann. Inference 139, 2459-2478]. We show that the estimator constructed using the stepsize which minimize the variance of the class of the recursive estimators defined in Mokkadem et al. (2009) gives the same pointwise LDP and MDP as the Rosenblatt kernel estimator. We provide results both for the pointwise and the uniform deviations.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:math/0601429 by other author

The stochastic approximation method for the estimation of a multivariate probability density

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.Comment: 28 page

Les travailleurs immigrants sélectionnés et l'accès à un emploi qualifié au Québec

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