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

• DOI: 10.1016/j.jspi.2008.11.012
• Publication Date: 2008-12-07T10:34:17Z
• Authors: Abdelkader Mokkadem; Mariane Pelletier; Yousri Slaoui
• Keywords: 62G07; 62L20; Mathematics - Statistics Theory; [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]; Statistics Theory (math.ST); 02 engineering and technology; [STAT]Statistics [stat]; Density estimation; MSC : 62G07 (62L20); [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; 62G07; FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; Stochastic approximation algorithm; 62L20; [STAT.ME]Statistics [stat]/Methodology [stat.ME]; [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]

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.<br/>28 pages<br/>