Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data. (6th March 2019)

• Record Type: Journal Article
• Authors: Guo, Huijun; Kou, Junke
• Other Names: Curto Raúl E. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2019(2019)
• Publication Date: 2019-03-06
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2019/7102346
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper considers the strong uniform convergence of multivariate density estimators in Besov spaceB p, q s ( R d ) based on size-biased data. We provide convergence rates of wavelet estimators when the parametricμ is known or unknown, respectively. It turns out that the convergence rates coincide with that of Giné and Nickl's ( Uniform Limit Theorems for Wavelet Density Estimators, Ann. Probab., 37(4), 1605-1646, 2009 ), when the dimensiond = 1, p = q = ∞, andω ( y ) ≡ 1 .