The Study Of Several Types Of Linear Statistical Models Based On Deletion Of Data Optimization

Linear models with a wide range of applications in statistics. During the actual problem research, case-deletion model or mean-shift outlier model has been applied, the researchers by observing the change of statistical magnitude, such as students residuals si, Cook distance and likelihood distance, etc., before and after the ith observation to be deleted to identify whether the point is outliers or influential case, that is, whether the point should be deleted from the given data set D. The basic principle of stepwise regression or backward method has been applied, the researchers by observing the change of the regression coefficients and leverage value, etc., before and after the j th independent variable to be deleted to distinguish whether the j th independent variable have significant to regression equation, in order to make a decision that the j th independent variable to be deleted or maintained. Fact whether the selection process for the identification of outliers or influential point or independent variable selection, is a dynamic, interrelated processes.On the basis of previous studies, this paper made a detailed analysis about the linear model with the nonhomogeneous random error term, the basic principle of mean-shift outlier model and stepwise regression method has been applied, when an observation and a independent variable to be deleted simultaneous. Its main purpose is to explore the size of each observations contribute as well as the contribution of each independent variable is.Linear model divided into four cases studied, that is, total-data model, select-data model, total-mean-shift outlier model and election-mean-shift outlier model. Then, the impact analysis from the leverage value of ith observation, the residual sum of squares, the fitted values and partial F tests were carried out on election-mean-shift outlier model.First, based on the research of the leverage value of the ith observation, found that the value that is the leverage value of the ith observation (yi χ’i|j|) of election-mean-shift outlier model is equal to δwij2, indicate that the j th independent variable’s contribution to the ith observation. The potency pwij(i)(j), the ith observation (yi χ’i|j|) of projection matrix of election-mean-shift outlier model, indicate that the total change of the variance of the fitted values before and after the ith observation to be deleted. And the size of the potential and wii are closely related.Then, by the norm of the difference of the residual sum of squares between election-mean-shift outlier model and total-data model, abtain a n×k order matrix DRSS(?). Positive or negative, the values of the matrix’s the ij th element, representation of the ith observation and the j th independent variable affect on the established model, that is, if the ij th element is negative, it indicates that for a postulated model, the i th observation than the j th independent variable have a more significant impact.Then, it obtained that standardized form of prediction error of election-mean-shift outlier model, DPRDwij, through the analysis of election-mean-shift outlier model’s fitted values.Finally, biasing partial F-test between the four models, there is obtained statistics for a variety of situations.