Point-wise estimation for anisotropic densities

被引：18

作者：

Liu, Youming ^{[1
]}

Wu, Cong ^{[1
]}

机构：

[1] Beijing Univ Technol, Dept Appl Math, Beijing 100124, Peoples R China

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2019年 / 171卷

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

Adaptivity; Anisotropic density; Local Holder condition; Optimality; Point-wise estimation; WARPED BASES; CONVERGENCE;

D O I：

10.1016/j.jmva.2018.11.014

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper considers point-wise estimation of density functions under the local anisotropic Holder condition by the wavelet method. A linear wavelet estimate is first introduced and shown to be optimal. A data driven version is provided for adaptivity and the influence of the dimension is reduced under the independence structure of the estimated density. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：112 / 125

页数：14

共 21 条

[11] BANDWIDTH SELECTION IN KERNEL DENSITY ESTIMATION: ORACLE INEQUALITIES AND ADAPTIVE MINIMAX OPTIMALITY [J].

Goldenshluger, Alexander ;

Lepski, Oleg .

ANNALS OF STATISTICS, 2011, 39 (03) :1608-1632

[12]

Hardle W., 1998, WAVELETS APPROXIMATI

[13] DENSITY-ESTIMATION IN BESOV-SPACES [J].

KERKYACHARIAN, G ;

PICARD, D .

STATISTICS & PROBABILITY LETTERS, 1992, 13 (01) :15-24

[14] Wavelet optimal estimations for a density with some additive noises [J].

Li, Rui ;

Liu, Youming .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2014, 36 (03) :416-433

[15] Convergence order of wavelet thresholding estimator for differential operators on Besov spaces [J].

Liu, Youming ;

Wang, Huiying .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2012, 32 (03) :342-356

[16] GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS [J].

Lounici, Karim ;

Nickl, Richard .

ANNALS OF STATISTICS, 2011, 39 (01) :201-231

[17] Density deconvolution based on wavelets with bounded supports [J].

Pensky, M .

STATISTICS & PROBABILITY LETTERS, 2002, 56 (03) :261-269

[18] Pointwise adaptive estimation of a multivariate density under independence hypothesis [J].

Rebelles, Gilles .

BERNOULLI, 2015, 21 (04) :1984-2023

[19]

Triebel Hans, 2006, Monographs in Mathematics, V100

[20]

Tsybakov AB, 2009, SPRINGER SER STAT, P1, DOI 10.1007/978-0-387-79052-7_1

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