| In statistics, linear regression model is a kind of significant model, the least square estimate is the most common methods in estimated regression coefficients. The least square estimate have some excellent characters. However, not all situations can get ideal result. When design matrix X is pathological, the function of the least square estimate may be bad. The value of MSE is very big. To estimate the range of fluctuation will be greatly increased, therefore the accuracy of the results will be poor. In various applications, symbol is not consistent with actual of the phenomenon often happens. But in real life, especially when dealing with large regression problems, a complex collinearity phenomenon is inevitable. Therefore, in view of the situation, the statisticians seek the method that improved the least square estimate. The biased estimation is put forward in solving complex collinearity issues indicate a effective direction.Biased estimate abandons the feature that the value of estimation is unbiased, because of the decrease of the variance. Thus realized some excellent properties of the least square estimate is worse than biased estimate, this contributes its power to a large number of practical problems is solved. In this paper statistics on the achievements of before scholars, the history of biased estimates are reviewed, enhanced our understanding of biased estimation. This paper also summarizes the there widely used biased estimates:Stein estimatesã€PCE and RR, there properties are also inducted, and widely used generalized ridge estimates is improved in the biased estimate.Past research more concentrated on generalized ridge estimates is on the design matrix exist complex collinesrity. GRR is improved in this paper, assumptions are generalized to non full rank. Assumptions will be further expand. In the paper GRR is dinationed in both cases, and demonstrates with the excellent nature. Show that both the improved estimates is compressed, is linear transformation of LS estimates and all is biased estimates. Under MSE, showing the estimates is promoted is super to LS estimates.Assumptions is relax,more in line with the actual situation. |
