Evaluation On The Effect Of Independent Variable Selection In Linear Model On Estimator

The linear model is a general term of statistical models,including linear regression model, analysis of variance model etc. It is also a common model in modern statistics. Because of its rich theory and wide application, the linera model is applied to many fields such as agriculture, industry, economics, management, meteorology, geology, biology, medicine, engineering and technique.In practice, it is necessary to find a reasonable independent variable to create a linear model. However, dependent variables are usually related to many independent variables, which makes it very difficult to establish linear model. Statisticians have put forward many independent variable selection criterions to solve how to select suitable ones from a number of independent variables in a linear equation.On the basis of the previous study results, the author does further research of the selection of independent variable. It briefly introduces some independent variable selection criterions, for instance, residual mean squares, prediction of the variance of the deviation, prediction mean square error Sq, Cp criterion, prediction sum error of square and so on. And it proves the advantage of independent variable selection on evaluation and prediction with the variance and mean square error.The author evaluates the effect of independent variable selection on the least squares estimator with risk functions in classical linear model and generalized linear model. It further proves the increased accuracy of the least squares estimator after eliminating independent variable which has smaller effect on dependent variabley.