The mean consistency of wavelet estimators for convolutions of the density functions

被引：1

作者：

Guo, Huijun ^{[1
,2
]}

Wang, Jinru ^{[1
]}

Tian, Xinyan ^{[1
]}

机构：

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

[2] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Guangxi, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 343卷

基金：

中国国家自然科学基金;

关键词：

Density convolution; Wavelet; L-p-consistency; Noise; DECONVOLUTION;

D O I：

10.1016/j.cam.2018.04.045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In practical applications, people sometimes do not know whether the estimated function is smooth, and it is reasonable to consider the consistency of an estimator. Furthermore, the acquired data are usually contaminated by various random noises. In this paper, we develop the wavelet estimators for m-fold convolutions of the unknown density functions and consider their Lp (1 <= p <= infinity) consistency under noiseless and additive noise situations, respectively. Finally, simulation studies illustrate the good performances of our nonparametric wavelet estimators. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：1 / 11

页数：11

共 50 条

[41] SMOOTH ESTIMATORS OF DISTRIBUTION AND DENSITY-FUNCTIONS
LEJEUNE, M
SARDA, P
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1992, 14 (04) : 457 - 471
[42] Wavelet characterization of functions with conditions on the mean oscillation
Aimar, H
Bernardis, A
WAVELET THEORY AND HARMONIC ANALYSIS IN APPLIED SCIENCES, 1997, : 15 - 32
[43] Approximating probability density functions and their convolutions using orthogonal polynomials
Badinelli, RD
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1996, 95 (01) : 211 - 230
[44] On the L1-consistency of wavelet density estimates
Chacón, JE
Rodríguez-Casal, A
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2005, 33 (04): : 489 - 496
[45] Convergence Rates of Wavelet Density Estimators for Strongly Mixing Samples
Cui, Kaili
Kou, Junke
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021, 47 (03) : 701 - 723
[46] Convergence Rates of Wavelet Density Estimators for Strongly Mixing Samples
Kaili Cui
Junke Kou
Bulletin of the Iranian Mathematical Society, 2021, 47 : 701 - 723
[47] Strong uniform consistency rates of kernel estimators of cumulative distribution functions
Cheng, Fuxia
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (14) : 6803 - 6807
[48] A quadratic approximation for Jackknife estimators of the variance of sample mean functions
Cubeddu, C
Targhetta, ML
STATISTICAL PAPERS, 1999, 40 (01) : 1 - 12
[49] A quadratic approximation for Jackknife estimators of the variance of sample mean functions
C. Cubeddu
M. L. Targhetta
Statistical Papers, 1999, 40 : 1 - 12
[50] INTEGRATED CONSISTENCY OF SMOOTHED PROBABILITY DENSITY ESTIMATORS FOR STATIONARY-SEQUENCES
CASTELLANA, JV
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 33 (02) : 335 - 346

← 1 2 3 4 5 →