Wavelet Optimal Estimations for a Multivariate Probability Density Function Under Weighted Distribution

被引:3
|
作者
Chen, Lei [1 ]
Chesneau, Christophe [2 ]
Kou, Junke [3 ]
Xu, Junlian [4 ]
机构
[1] Baoji Univ Arts & Sci, Sch Phys & Optoelect Technol, Baoji, Peoples R China
[2] Univ Caen Normandie, LMNO, Campus 2,Sci 3, F-14032 Caen, France
[3] Guilin Univ Elect Technol, Sch Math & Computat Sci, Guilin, Peoples R China
[4] Baoji Univ Arts & Sci, Sch Math & Informat Sci, Baoji, Peoples R China
基金
中国国家自然科学基金;
关键词
Point-wise function estimation; wavelet estimator; multivariate probability density function; weighted distribution; data driven; holder space;
D O I
10.1007/s00025-023-01846-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The purpose of this paper is the pointwise estimation of a multivariate probability density function with weighted distribution using wavelet methods. New theoretical contributions are provided; Point-wise convergence rates of wavelet estimators are established in the local Holder space. First, a lower bound is provided for all the possible estimators. Specially, a linear wavelet estimator is defined and turned out to be the optimal one in the considered setting. Subsequently, regarding the adaptive estimation problem, a nonlinear estimator is proposed as usual and discussed. Finally, a new data driven wavelet estimator is introduced and shown to be completely adaptive and almost optimal.
引用
收藏
页数:21
相关论文
共 50 条
  • [31] MONOTONICITY OF THE PROBABILITY OF A RECTANGULAR REGION UNDER A MULTIVARIATE NORMAL-DISTRIBUTION
    BOLVIKEN, E
    JOAGDEV, K
    SCANDINAVIAN JOURNAL OF STATISTICS, 1982, 9 (03) : 171 - 174
  • [32] Multilook polarimetric SAR data probability density function estimation using a generalized form of multivariate K-distribution
    Bian, Yong
    Mercer, Bryan
    REMOTE SENSING LETTERS, 2014, 5 (07) : 682 - 691
  • [33] Sampling the Multivariate Standard Normal Distribution under a Weighted Sum Constraint
    Vrins, Frederic
    RISKS, 2018, 6 (03):
  • [34] Reliability estimations of generalized exponential distribution under entropy loss function
    Yan, Wei-An
    Shi, Yi-Min
    Sun, Tian-Yu
    Wang, Liang
    Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice, 2011, 31 (09): : 1763 - 1769
  • [35] Nonparametric Method for Estimating Spoken Language Sound Multivariate Probability Density Function
    Bokal, Zanna A.
    Sinitsyn, Rustern B.
    MRRS: 2008 MICROWAVES, RADAR AND REMOTE SENSING SYMPOSIUM, PROCEEDINGS, 2008, : 170 - 171
  • [36] Statistical Image Modeling with the Magnitude Probability Density Function of Complex Wavelet Coefficients
    Rakvongthai, Yothin
    Oraintara, Soontorn
    ISCAS: 2009 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOLS 1-5, 2009, : 1879 - 1882
  • [37] Higher-order statistics and the multivariate probability density function of natural images
    Zetzsche, C.
    Krieger, G.
    Roehrbein, F.
    PERCEPTION, 2000, 29 : 82 - 82
  • [38] Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values
    Al-Duais, Fuad S.
    COMPLEXITY, 2021, 2021
  • [39] Investigation of wind power density distribution using Rayleigh probability density function
    Paraschiv, Lizica-Simona
    Paraschiv, Spiru
    Ion, V. Ion
    TECHNOLOGIES AND MATERIALS FOR RENEWABLE ENERGY, ENVIRONMENT AND SUSTAINABILITY (TMREES), 2019, 157 : 1546 - 1552
  • [40] Estimation methods for the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution
    Jebeli, Maleki
    Deiri, E.
    STATISTICS, 2020, 54 (01) : 135 - 151