Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data

Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data

This paper considers the strong uniform convergence of multivariate density estimators in Besov space Bp,qs(Rd) based on size-biased data. We provide convergence rates of wavelet estimators when the parametric μ is known or unknown, respectively. It turns out that the convergence rates coincide with...

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Main Authors: Huijun Guo, Junke Kou
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/7102346
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spelling doaj-cfd7b8c253494ea997a68a5c968f3a812020-11-25T02:21:25ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/71023467102346Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased DataHuijun Guo0Junke Kou1School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, ChinaSchool of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, ChinaThis paper considers the strong uniform convergence of multivariate density estimators in Besov space Bp,qs(Rd) based on size-biased data. We provide convergence rates of wavelet estimators when the parametric μ 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 dimension d=1, p=q=∞, and ω(y)≡1.http://dx.doi.org/10.1155/2019/7102346
collection DOAJ
language English
format Article
sources DOAJ
author Huijun Guo
Junke Kou
spellingShingle Huijun Guo
Junke Kou
Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
Journal of Function Spaces
author_facet Huijun Guo
Junke Kou
author_sort Huijun Guo
title Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
title_short Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
title_full Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
title_fullStr Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
title_full_unstemmed Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
title_sort strong uniform convergence rates of wavelet density estimators with size-biased data
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2019-01-01
description This paper considers the strong uniform convergence of multivariate density estimators in Besov space Bp,qs(Rd) based on size-biased data. We provide convergence rates of wavelet estimators when the parametric μ 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 dimension d=1, p=q=∞, and ω(y)≡1.
url http://dx.doi.org/10.1155/2019/7102346
work_keys_str_mv AT huijunguo stronguniformconvergenceratesofwaveletdensityestimatorswithsizebiaseddata
AT junkekou stronguniformconvergenceratesofwaveletdensityestimatorswithsizebiaseddata
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