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基于乘法噪声模型构造出新的硬阈值小波估计器，并定义了一类特殊的密度函数集，针对该密度函数集在各向异性Besov空间上讨论了非紧支偏差密度函数的L1风险估计，最终得到相应的L1收敛阶。更重要的是，硬阈值估计器相对于线性估计器已经达到了自适应的效果。
Abstract：This study constructs a new hard thresholding wavelet estimator based on the biased data and defines a special category of density function sets, for which the L1 risk estimation of uncompactly supported biased density functions on anisotropic Besov spaces is discussed, and the corresponding L1 convergence is obtained. More importantly, the hard thresholding estimator has achieved the adaptive effect relative to the linear estimator.
[1]Devroye L,Gyorfi L.Nonparametric density estimation:the L1 View[M].New York:Wiley,1985.
[2]Daubechies I.Ten lectures on wavelets[M].U.S.:Society for industrial and applied mathematics,1992.
[3]Donoho D L,Johnstone I M,Kerkyacharian G,et al.Density estimation by wavelet thresholding[J].The Annals of Statistics,1996,24(2):508～539.
[4]Delyon B,Juditsky A.On minimax wavelet estimators[J].Applied and Computational Harmonic Analysis,1996,3(3):215～228.
[5]Kerkyacharian G,Picard D.Density estimation in Besov spaces[J].Statistics probability letters,1992,13(1):15～24.
[6]曹凯凯.各向异性密度函数的小波估计[J].山东大学学报 (理学版),2019,54(6):99～105.
[7]Juditsky A,Lambert-Lacroix S.On minimax density estimation on R[J].Bernoulli,2004,10(2):187～220.
[8]Goldenshluger A,Lepski O.On adaptive minimax density estimation on Rd [J].Probability Theory and Related Fields,2014,159(3-4):479～543.
[9]Chesneau C.Wavelet block thresholding for density estimation in the presence ofbias.Journal of the Korean Statistical Society,2010,39(1):43～53.
[10]Xu J.Wavelet thresholding estimation of density derivatives from a negatively associated size-biased sample[J].International Journal of Wavelets,Multiresolution and Information Processing,2020,18(3):23～27.
[11]Chen L,Chesneau C,Kou J,et al.Wavelet Optimal Estimations for a Multivariate Probability Density Function Under Weighted Distribution[J].Results in Mathematics,2023,78(2):66.DOI:https://doi.org/10.1007/s00025-023-01846-1.
[12]Cao K,Liu Y.Uncompactly supported density estimation with L1 risk[J].Communications on Pure Applied Analysis,2020,19(8):4007～4022.
[13]曹凯凯，梁志刚，曾晓晨.高维非紧支密度函数的小波硬阈值估计[J].数学进展，2022,(6):1075～1092.
[14]Triebel H.Theory of function spaces Ⅲ [M].Basel:Birkhauser-Verlag,2006.
[15]Meyer Y.Wavelets and Operators[M].Cambridge:Cambridge University Press,1992.
[16]Kou J,Liu Y.Non parametric regression estimation over Lp risk based on biased data[J].Comm.Statist.Theory Methods,2017,46(5):2375～2395.
[17]Reynaud-Bouret P,Rivoirard V,Tuleau-Malot C.Adaptive density estimation:a curse of support?[J].Journal of Statistical Planning and Inference,2011,141(1):115～139.
[18]H?rdle W,Kerkyacharian G,Picard D,et al.Wavelets,approximation,and statistical applications[M].New York:Springer,1998.
基本信息:
DOI：
中图分类号:O212.1
引用信息:
[1]许俊莲,朱亚玲.各向异性非紧支偏差密度函数的L~1风险估计[J].湖北师范大学学报(自然科学版),2025,45(02):7-20.
基金信息:
国家自然科学基金青年资助项目(12101014); 宝鸡文理学院校级研究生创新科研项目(YJSCX24YB37)