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

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

2008-07-18

arxiv.org/abs/0807.2960v1

Mathematics

Statistics Theory

28 pages

Scientific paper

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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