On The Stochastic Restricted S-K Estimator And Principal Components S-K Class Estimator

Linear model is a basic model in mathematical statistics and be-comes an important research branch of modern statistics because of its rich content, wide use. And the discussion about parameter estimation is a fundamental work to investigate the linear model. Overcoming multicollinearity in the linear model has always been the hot spot in statistics. A common method is to apply biased estimators. However, autocorrelation problems in the linear model are can not be ignored. Now the research to solve autocorrelation and multicollinearity prob-lems simultaneously is getting more and more importance.This paper studied the stochastic restricted s-K estimator and principal components s-K class estimator in the linear model. We obtained the sufficient and necessary conditions that the new estimators are superior to the other estimators, and gived numerical simulation.The paper is made up of four parts. In the first part, we sketched background and progress in studies of biased estimators, and also pro-vided the preliminary knowledge related to this paper. In the second part, we put forward a new class of stochastic restricted s-K estimator in the linear model, and discussed the comparisons in the mean square error matrix standard. In the third part, we proposed a stochastic re-stricted s-K estimator in the linear model with correlated errors, and obtained the sufficient and necessary conditions that the new estima-tors are superior to the other estimators. In the fourth part, we offered principal components s-K class estimator in the linear model with cor- related errors, and proved excellent performance of the new estimator in the mean square error matrix sense.