Semiparametric Additive Model Of Liu Estimation

Over the last two decades,Semiparametric model which was used to solve the problems,has received more and more attention by Statisticians and Econometricians.A useful extension of Semiparametric model is the Semiparametric additive model, it inherits the advantages of Semiparametric model, in which some of the additive component functions are parametric terms while the remaining ones are modelled nonparametrically. one unknown smoothing parameter in Semiparametric model is generalized to multiple unknown smoothing parameter in Semiparametric additive model. Semiparametric additive model is more complex than the Semiparametric model, but it is more persuasive to explain the practical problems.Ospomer and Ruppert(1999)proposed a backfitting estimator for parametric component in Semiparametric additive model. Liang et al(2008) proposed a Profile estimator of the parametric component with the simple case of q=2.Wei(2012) studied multiple unknown smoothing parameter estimator in Semiparametric additive model. In some practical problems,researchers often encounter the problem of multicollinearity, there are many ways to solve multicollinearity problem in the classic linear model, however, there are few papers about dealing with the multicollinearity problem in Semiparametric additive model.In year2009, Akdeniz and Duran introduced a Liu-type estimator for the parametric component in a semiparametric regression model,and the theory property had been proved better than other estimators.In this paper,when parametric component encounter the problem of multicollinearity,the paper is organized as follows.The second chapter,Profile least-square Liu estimation in Semiparametric additive model is proposed.we discuss its property under mean square error(MSE) and prove that Profile least-square Liu estimation is better than ordinary Profile least-square when it satisfy certain conditions.The third chapter, Profile least-square generalized Liu estimation in Semiparametric additive model is proposed, we discuss its conditions when it is better than Profile least-square Liu estimation under mean square error(MSE).The fourth chapter,we assume that the additional conditions on the parametric component are of Aβ=b,constructing restricted profile least-squares Liu estimation.it prove that a real number d is existence in order to βRPLSL(d)is better than the restricted ordinary profile least-squares estimation βRPLS under mean square error(MSE).The fifth chapter, additional linear stochastic constraints can be added with the constraints of the Semiparametric model,we construct a new Profile least-square Liu estimation and proved that it is superior to the restricted ridge estimation and ordinary least squares estimation under mean square error(MSE).The sixth chapter,we construct Backfitting-Liu estimation and restricted Backfitting-Liu estimation in Semiparametric additive model.The seventh chapter,we study Monet Carlo simulation with R software.