基于强混偏差样本的各向异性回归函数小波估计的相合性分析  

Consistency of Wavelet Estimation of Anisotropic Regression Functions Based on Samples with Strong Mixed Bias

作　　者：陈佳 Chen Jia(School of Mathematics,Sichuan University of Arts and Sciences,Dazhou 635000,China)

机构地区：[1]四川文理学院数学学院,四川达州635000

出　　处：《黑龙江科学》2023年第24期62-64,68,共4页Heilongjiang Science

基　　金：四川文理学院校级科研项目(2022QD06)。

摘　　要：针对强混条件下各向异性回归函数的估计问题,利用小波独特的局部时频分析特性构造了线性小波回归估计器,并在B_(p,q)~s(R~d)空间中讨论了L~p(1≤p<∞)误差意义下的相合性。研究结果表明,在样本容量充分大时,小波估计量■能够满足任何精度,当空间B_(p,q)~s(R~d)的各向异性指标相等时,结论与各向同性Besov空间中的结果保持一致。Aiming at the estimation of anisotropic regression function under strong mixing conditions,a linear wavelet regression estimator is constructed using the unique local time-frequency analysis characteristics of wavelet,and its consistency in the sense of L p(1≤p<∞)error is discussed in B,q(R d)space.The results show that the wavelet estimator jτ(x)can satisfy any accuracy when the sample size is large enough,and the conclusion is consistent with the results in isotropic Besov space when the anisotropy index of space B,q(R d)is equal.

关 键 词：回归估计 强混样本 各向异性 相合性 

分 类 号：O174.2[理学—数学] O212.7[理学—基础数学]