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

Abdelkader Mokkadem (1, 2) , Mariane Pelletier (2) , Yousri Slaoui (2)

1 Technocentre Renault [Guyancourt]
2 LMV - Laboratoire de Mathématiques de Versailles

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.

Domaines: Théorie [stat.TH]; Méthodologie [stat.ME]

Abdelkader Mokkadem, Mariane Pelletier, Yousri Slaoui. The stochastic approximation method for the estimation of a multivariate probability density. Journal of Statistical Planning and Inference, 2009, 139 (7), pp.2459-2478. ⟨10.1016/j.jspi.2008.11.012⟩. ⟨hal-00672833⟩