Consistency of multivariate density estimators using random bandwidths. Issue 2 (17th January 2016)

• Record Type: Journal Article
• Authors: Dutta, Santanu; Saha, Koushik
• Is Part Of: Communications in statistics. Volume 45:Issue 2(2016)
• Page Start: 252
• Page End: 266
• Publication Date: 2016-01-17
• Subjects: Multivariate kernel density estimate -- L1 distance -- Cross-validation; 62G07 -- 62G09 -- 62G20; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2013.830747
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract : Asymptotic properties of a kernel density estimator using a random bandwidth are difficult to establish. Under some assumptions we prove the L 1 consistency of a class of multivariate kernel density estimators using different bandwidth vector selectors. The expected L 1 distance between such an estimator and the density is also shown to converge to zero. Our results hold even when the marginal densities are heavy-tailed. As a special case, we propose a simple estimator that depends on only one parameter, irrespective of the dimension. Its L 1 distance from the density goes to zero, exponentially. Simulations suggest that this estimator performs well in terms of the integrated squared error as well.