Berry-Esseen Bounds For Wavelet Estimator Of Regression Models Under Mixing Process

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.