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On the L_p Convergence Rate of Kernel Estimates for the Nonparametric regression function

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Chinese Quarterly Journal of Mathematics 1992年第1期7卷 37-43页

作者：薛留根河南许昌师范专科学校

Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive... 详细信息

Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng.

关键词： regression function L convergence rate kernel estimate

Nonparametric regression with Interval-Censored Data

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Acta Mathematica Sinica,English Series 2014年第8期30卷 1422-1434页

作者： Wen Li DENG Zu Kang ZHENG Ri Quan ZHANG School of Mathematics and Information Science Jiangxi Normal University Department of Statistics School of ManagementFudan University Department of Statistics School of Finance and StatisticsEast China Normal University

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a *** nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods *** the censored data,we construct a new response variable which has the same conditional expectation as the original *** on the new variable,we get a nearest neighbor estimator of the regression *** is established that the estimator has strong consistency and asymptotic *** relevant simulation reports are given.

关键词： Interval-censored data regression function nearest neighbor estimator

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC regression MODEL

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Applied Mathematics(A Journal of Chinese Universities) 2007年第4期22卷 453-459页

作者： Liang Hanying Lu Yi Dept. of Appl. Math. Tongji Univ. Shanghai 200092 China.

The following heteroscedastic regression model Yi = g（xi）＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.

关键词： regression function martingale difference error wavelet estimator asymptotic normality.

Wavelet Neural Networks and its Application Research

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Wavelet Neural Networks and its Application Research