Biased Estimates Of The Parameter In Semi-Varying Coefficient Regression Model

Semi-variable coefficient regression model is an important model in statistics,which is widely used in natural science,finance,economy and other fields.The estimation of unknown parameters in the model is one of the hot issues studied by statisticians.Fan et al.proposed profile least squares estimation based on local linear fitting method.However,when there is a problem of complex collinearity among constant coefficient variables in the model,the property of the profile least squares estimation is no longer good.In this paper,three kinds of biased estimation of parameters are proposed based on profile least squares estimation for the problem,and the properties of the three estimations are discussed under the criterion of mean square error,mean square error matrix,etc.Firstly,Liu estimation of parameters in semi-variable coefficient regression model is proposed,and its basic properties are discussed;under the criterion of mean square error,the sufficient and necessary condition that Liu estimation is better than the profile least square estimation is given;Monte Carlo simulation is used to verify the superiority of Liu estimation.Secondly,by combining Liu estimation with the idea of almost unbiased,the almost unbiased Liu estimation of parameters in semi-variable coefficient regression model is proposed,and some basic properties are discussed;under the criterion of mean square error,the sufficient conditions that the almost unbiased Liu estimation is better than the profile least squares estimation,ridge estimation and Liu estimation are given;under the criterion of mean square error matrix,the sufficient and necessary condition that the almost unbiased Liu estimation is better than the almost unbiased ridge estimation is given;Monte Carlo simulation is used to verify the superiority of the almost unbiased Liu estimation.Finally,by combining Liu estimation with ridge estimation,the two parameter estimation of parameters in semi-variable coefficient regression model is proposed.It is a generalized form of the profile least squares estimation,Liu estimation and ridge estimation;under the criterion of mean square error matrix,the sufficient and necessary conditions for the two parameter estimation to be superior to profile least squares estimation,ridge estimation and Liu estimation are given;the method of selecting optimal value of parameter k and d in the estimation is given.Monte Carlo simulation is used to verify the superiority of the two parameter estimation.