【作者】 韦程东；

【导师】 刘妍岩；

【作者基本信息】 武汉大学 ， 概率论与数理统计， 2013， 博士

【摘要】 本文在线性过程误差的假设下讨论了两个问题：一是非参数回归模型小波估计的Berry-Esseen界；二是半参数回归模型小波估计的Berry-Esseen界.第一部分考虑非参数回归模型Uni=g(tni)+εi,i=1,…,n,其中9(·)是定义在区间[0,1]上的未知函数,{tni}是非随机设计点列,{εi}是随机误差.假设εi是由φ混合序列生成的线性误差,其中aj为常数且满足为φ混合序列.在上述假设下,我们建立了9(·)的小波估计的Berry-Esseen界.第二部分考虑半参数回归模型Yi=xiβ+9(ti)+εi,i=1,…,n,此处β是一未知参数,g(·)是定义在区间[0,1]上的未知函数,{(xi,t)}是非随机设计点列,{Yi}是响应变量,{εi}是随机误差.假设εi是由强混合序列生成的线性误差,即其中aj为常数且满足：为强混合序列.在上述假设下,我们建立了未知参数β和g(·)的小波估计的Berry-Esseen界.更多还原

【Abstract】 This dissertation addresses two issues under linear process errors:Berry-Esseen bounds for wavelet estimator in nonparametric regression model and semiparametric regression model.In the first section, we consider the following nonparametric regression model:Yni=g(tni)+εi, i=1,…,n,were g(·) is an unknown function defined on the closed interval [0,1],{tni} are nonrandom design points,{εi} are random errors. Suppose that εi be an linear error generated by φ mixing, that is to say with∞, and {ei} are φ mixing.the Berry-Esseen type bound of wavelet estimator for the unknown function g(·) is established under the above assumption.In the second section, we consider the following semiparametric regres-sion model:Yi=xiβ+g(ti)+εi,i=1,…,n,where β is an unknown param-eter of interest,{(xi, ti)} are nonrandom design points,{Yi} are the response variables, g(·) is an unknown function defined on the closed interval [0,1], and{εi} are random errors. Suppose that εi be an linear error generated by strong mixing, that is to say with and {ei} are strong mixing, the Berry-Esseen type bound of wavelet estimator for the unknown parameter β and the unknown function g(·) are established under the above assumption.更多还原