Research On Biased Estimation Based On Difference Method In Semiparametric Model

Due to the influence on the accuracy of the statistical model,parameter estimation becomes one of the principal parts in establishing a statistical model.The semiparametric model contains the information of the parameter part and the non-parameter part.It has strong adaptability in practical applications.At present,there are many practical parameter estimation methods that are cited in the semiparametric model.Nevertheless,in this paper,we mainly study the classical theory in some linear models in the case of problems concerning multicollinearity.From this point of view,the difference-based method is used in this paper to eliminate the influence of non-parametric parts by using a higher-dimensional difference matrix,furthermore,two new types of differential-based estimates are proposed,and their superiority is discussed under the MSEM and MSE criteria,and finally verify the correctness of the theory.Considering that the design matrix has strong or weak multicollinearity in the semiparametric model,the paper firstly proposes a modified estimation based on the difference,that is,a difference-based modified ridge estimate and a difference-based modified Liu estimate.The analysis is divided into two angles.One is to proceed from the properties of the proposed difference-based modified estimate.The statistical properties based on the difference-based modified estimation are discussed.The other is based on the MSEM criterion,the superiority of the difference modified estimations is compared with the difference-based least squares estimation,difference-based ridge estimation and difference-based Liu estimation under conditions.the performance of the new estimators is evaluated for some numerical simulations and example.Furthermore,based on a new Liu estimate is proposed by Kurnaz and Akay,using a differencing method,a difference-based new Liu estimate is put forward in a semiparametric model.This estimator is bias,that is a generalized form of the differencebased least-squares estimator,ridge estimator,and Liu estimator and could solve the multicollinearity problem.Besides,a method of solving f(k)is given in this article: f(k)=ak +b,though optimization MSE(mean square error).In addition,the differencebased new Liu estimator compare the proposed estimators in the MSE criteria.Finally,simulation studies are presented to show the performance of the estimator.