Ridge Estimation Of Partial Linear Variable Coefficient

In order to fit the data better, people have put forward many forms of non-parametric regression model, including variable coefficient regression model which not only can maintain the flexibility of nonparametric regression model, but also can overcome the curse of dimensionality. As a promotion of variable coefficient regression model, partially linear varying coefficient model reflects a more precise structure of the regression function, provides more detailed information to analyze and understand the impact of independent variables on the dependent variable, which has been widely used.About partially linear varying coefficient model, the research focus on parameters section, but current estimation method, no matter it based on which smooth technology, but also suppose there is no multicollinearity between independent variables however, in actual data analysis, multicollinearity is a common problem, so how to overcome the multicollinearity is an important part of regression analysis. It is well known, for ordinary linear regression model, constructing biased estimation to get a smaller mean square error is a common method. Ridge Estimator and Principal Components Estimate are most frequent in textbooks. However most biased estimates and multicollinearity discussions are based on the general linear regression model, so for partially linear varying coefficient model, how to overcome multicollinearity and construct biased estimate is a very meaningful topic. However, there is very little correlation results. In practical and theoretical points, studying partially linear varying coefficient models how to overcome multicollinearity problem and how to construct a biased estimate is meaningful.This article assumes that partially linear varying coefficient model appears multicollinearity, mainly to do the following work:The second part construct a profile least-squares ridge estimation in partially linear varying coefficient model, and prove that under certain conditions, profile least-squares ridge estimation is better than profile least-squares estimation under mean square error, and make a numerical simulation to the model;In the third part, this article assumes that model parameters exist linear equations restrict, construct a restricted profile least-squares ridge estimation in partially linear varying coefficient model, and prove that under certain conditions, restricted profile least-squares ridge estimation is better than restricted profile least-squares estimation under mean square error, and make a numerical simulation to the model;In the fourth part, this article assumes that model parameters exist stochastic linear restrict, construct a stochastic restricted profile least-squares ridge estimation in partially linear varying coefficient model, study some properties of estimation and make a numerical simulation to the model;...