Biased Estimation And Excellent Standards

Linear regression model analysis is very important in the theory of a class of mathematical models in modern statistics,its basic theory has become one of the basic tools of other statistical research,the parameter estimation problem is that many scholars have paid special attention to the problem.With the continuous research on the parameter estimation problem,many research results have said that the traditional sense of the least squares estimation in solving many problems,such as when the design matrix is ill conditioned,the effect of the least squares estimation worse and even failure.So it is no longer an optimal estimator.Therefore,there are many new estimators,such as ridge estimation,Stein estimation,Root Root Estimator and principal component estimation and so on.With the further development of research,many scholars began to parameters of ridge estimate is studied,and puts forward the method of choosing a ridge parameter.In this paper,we mainly study three problems of parameter estimation: first,Stein type root mean square estimation.First introduced the Stein type root root estimator is proposed as well as the Stein Root Root Estimator of some properties of Stein type root root estimator,and then proved that the Stein type root root estimator outperforms some other estimates by application examples.Second problems about the selection of ridge parameter selection method,introduces some parameters and the ridge ridge trace.The method was proved.Third,Universal Ridge Estimate and Stein square root under the criterion of estimation.The main discussion in the quality of estimation under two.