Outlier Analysis Of Linear Regression Model

Outlier is an important concept in statistical diagnose theory. The identification and treatment of outliers are the keys to the success of statistical diagnose, while the process of identification is the base of diagnose . Since the concept of outlier is brought up for the first time, the discuss of its concept, types, identification and treatment never stop. This article mainly LAD model launched a linear regression model and the linear model of outlier identification issues, on the basis of summing up the work of our predecessors, for the promotion and application of LAD has been the result of the return series.Chapter 2 introduces the basic linear regression model, When the error obey normal distribution, constructing Statistics to take testing of one or more abnormal points hypothesis testing. There detailed account the equivalent role of case deletion model and mean shift outlier model in the testing anomalies. Chapter 3 presents the regression model and the basic nature of the LAD, In very general terms shows that the case deletion model and mean shift outlier model equivalence Theorem. In the LAD regression modelγ* mi =e?i(i), the results can properly explain the relationship between the case deletion model and mean shift outlier model, and the role of the two diagnostic model in Statistics diagnosis.The fourth chapter describes a number of diagnostic statistics applied to LAD regression models. Under the guidance of likelihood distance, by the enlightenment of likelihood ratio test statistic form, a new measure :Quasi-likelihood distance, It errors in the distribution of any request, breakthrough the limitations of likelihood distance in the LAD regression diagnostics. Also studied Cook distance of LAD regression diagnosis, influence measure FDi , FD1 iand so on. We know LAD regression resists outliers in the response variable but is relatively to outlying observations in the explanatory variables. Here, we used a simple solution to overcome this problem : change the deviation of horizontal direction to vertical direction's to treatment. Through data analysis shows that the actual results and the effectiveness of this theory and practical.