The stochastic approximation method for the estimation of a multivariate probability density |
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Authors: | Abdelkader Mokkadem Mariane Pelletier Yousri Slaoui |
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Institution: | Département de Mathématiques, Université de Versailles-Saint-Quentin, 45, Avenue des Etats-Unis, 78035 Versailles Cedex, France |
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Abstract: | 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. On the efficiency of on-line density estimators. IEEE Trans. Inform. Theory 40, 1504–1512]. 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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Keywords: | Density estimation Stochastic approximation algorithm |
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