Research On Several Types Generalized-Difference-Based Unbiased Estimators In Partially Linear Model

Partially linear model is an important semiparametric statistical model.Regarding the estimator of the linear part parameter vector in this model,the common method is using the difference-based method to convert the partially linear model into a linear model,and then uses the least square method to obtain the difference-based least squares estimator.In partially linear model with correlated errors,this paper considers the presence of random prior information about linear part parameter vectors in the model,several types of generalized-difference-based unbiased estimators are proposed,and superiority of each estimator is discussed in the mean square error matrix or mean square error criterion.For the estimator of linear part parameter vectors in partially linear model,this paper mainly proposes generalized-difference-based unbiased ridge estimator by combining with generalized-difference-based method and unbiased ridge estimator method about the random prior information of parameter vectors,and properties of the new estimator are discussed.At the same time,the superiority of generalized-difference-based unbiased ridge estimator relative to generalized-difference-based least squares estimator,generalized-difference-based ridge estimator,and generalized-difference-based almost unbiased ridge estimator is discussed in the sense of mean square error matrix.Finally,based on numerical simulation and empirical analysis method,the superiority of generalized-difference-based unbiased ridge estimator is explained in the sense of mean square error.This paper proposes generalized-difference-based unbiased Liu estimator based on the random prior information of parameter vectors by combining with generalized-differencebased method and unbiased Liu estimator method,and its properties are discussed.At the same time,conditions of generalized-difference-based unbiased Liu estimator are better than generalized-difference-based least squares estimator,generalized-difference-based Liu estimator,and generalized-difference-based almost unbiased Liu estimator that are deduced in the sense of mean square error matrix.Furthermore,this paper explains the superiority of the generalized-difference-based unbiased Liu estimator in the sense of mean square error through numerical simulation and empirical analysis method.This paper generalizes the generalized-difference-based unbiased ridge estimator and Liu estimator as more general generalized-difference-based unbiased two-parameter estimator,and conditions of generalized-difference-based unbiased two-parameter estimator are better than generalized-difference-based least squares estimator,generalized-difference-based two-parameter estimator and generalized-difference-based almost unbiased two-parameter estimator that are theoretically discussed under the mean square error matrix.At the same time,this paper studies its superiority in the sense of mean square error through the numerical simulation and empirical analysis method.