Estimation For Semiparametric Models And Methods

Semiparametric regression model is a emerging statistical branch in recent years, which combined the advantages of linear regression model and the nonparametric model, has important meaning in both theory research and applying research. In this paper, the properties of further research on semiparametric regression model are studied on the base of domestic and overseas scholar researches.Firstly, the semiparametric regression model is introduced from the origin to the development at home and abroad, including a several different forms of the model and different methods to study the property of the parameter estimation.Secondly, the p-th consistency of the estimation for parameterβand unknown function g(t_i) and 2p-th consistency of the estimation for error varianceσ~2 are discussed on the semiparametric model y_i=x_iβ+g(t_i)+V_i,V_i=σ_ie_i (1≤i≤n) under dependentcondition (errors are martingale difference sequence)of the stochastic errors. And the consistency of semiparametric model is obtained using the assumption and the operational rule of the martingale difference sequence.Finally, the estimator of parameterβis improved under the condition of the mean square errors on the semiparametric regression model Y=Xβ+g(t)+e,by the method of iteration, the dominating two-step estimator of parameterβis obtained, which can be proved superior than two-stage estimator with mean square error.