B-spline Estimation Of Single Index Variable Coefficient Model

In this dissertation,we focus on inference for a class of varying coefficient model by B-spline estimation,including varying coefficient model,partially linear varying coefficient model,single index varying coefficient model.More specifically,the research contents of this dissertation are summarized as follows.Under the least-squares,a new estimation method is proposed for varying coefficient model by B-spline approximations which is called two-step B-spline estimation.The first step is to obtain the number of knot required for different coefficient functions.The second step uses different numbers of knot to obtain the final estimate of the coefficient functions.Under some regularity conditions,the asymptotic normality property of the proposed estimation method is established.A simulation study show that the proposed method is effective,and to assess the finite sample performance of the proposed method.The single-index varying-coefficient model,having a more effective interpretation,can be seen as a generalization of the single-index model and the varying-coefficient mod-el.In this dissertation,B-spline approximation technique,profile least squares estimation and Levenberg-Marquardt algorithm is used to estimate the parameters and coefficien-t functions of single-index varying-coefficient model.At the same time,the estimated consistency and asymptotic normality are also given.The simulation results show that the proposed method is effective for the estimation of the single-index varying-coefficient model,and can improve the efficiency of the coefficient function estimation in the case of limited sample.A new composite quantile regression estimation(CQR)approach is proposed for par-tially linear varying coefficient models(PLVCM).The functional coefficients are estimated by B-spline approximations.Moreover,we propose a new variable selection procedure for PLVCM under composite quantile loss function with adaptive Lasso penalty.The major advantage of the proposed procedures over the existing ones is easy to implement using existing software,and it requires no specification of the error distributions.Under some regularity conditions,we show that the proposed procedure can be as efficient as the Oracle estimator,and establish the large sample properties of the proposed estimators.A simulation study and a real data analysis are presented to assess the finite sample performance of the proposed method.