Superiority Of Several Common Biased Estimators

Linear regression model,one of the early-developed branches of mathematical statistics,is an important statistics model,which has been widely applied in such fields as economy,biology,industry,agriculture,medicine,social sciences,etc.The study on its parameter estimate can be traced back to the early nineteenth century.Least Square Estimate(LS),the most basic and common unbiased estimate,has a superiority.However,with the development of the Theory of Admissibility and the study on Large-scale Regression containing many variables,Least Square Estimate has been found ineffective under certain circumstances.In order to acquire a more accurate estimate on respective parameters in some given situation,statisticians offer a series of biased estimates,such as Ridge estimater(Narrow Ridge estimater),Generalized Ridge estimater,Liu estimater,Integrated c-K Ridge estimater to improve Least Square estimater.The emergence of different estimate models is bound to bring about the comparison of them,as well as the criterion for comparison,such as,Mean Squared Errors Criteria.This paper makes a discussion on the comparison of commonly-used estimates under the above criterion.