Bias reduction in kernel density estimation. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Slaoui, Yousri
• Is Part Of: Journal of nonparametric statistics. Volume 30:Issue 2(2018)
• Page Start: 505
• Page End: 522
• Publication Date: 2018-04-03
• Subjects: Density estimation -- stochastic approximation algorithm -- smoothing -- curve fitting -- bias reduction; Primary: 62G07; 62L20 -- Secondary: 65D10; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2018.1442927
• Languages: English
• ISSNs: 1048-5252

Abstract

ABSTRACT: In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, 'The stochastic approximation method for the estimation of a multivariate probability density', J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.