A Comparative Study Of Outliers Detection Methods In Regression Analysis

Regression analysis is a method of statistical analysis for datas, itsaim is to study whether two or more variables are related,to study thecorrelation coefficient and correlation strength, and to establish themathematical model to predict and control what the researchers interestedin by observing specific variables. Since the theory of classical linearregression model was founded, it has been widely used in many fieldssuch as natural science and social science, and obtained manyachievements. But there will always be outliers when applied regressionanalysis, these outliers will directly affect whether the regression modelcan be a good fit with the the reality, as well as the accuracy of parameterestimation, stability of the model and other series matters involving theregression analysis itself. Therefore, the diagnosis and treatment ofoutliers is both theoretical and practical significance.Outliers diagnostics has been much concerned by scholars, but sofar, there is no a standard or widely applicable method. This paperdescribes two outliers diagnostics used widely—LS-based methods anddiagnostic methods based on robust regression. The paper first gives abrief introduction to the former methods, and such methods aresummarized,pointing out the defects of these methods when dealing withdifferent outliers. And then leads to the latter type of method,the focus ofthis paper is also to study outliers diagnostic methods based on robust regression analysis. Through simulation, the efficiency of several robustdiagnostic methods used commonly were compared to investigate themost effective diagnostic method in the case of different outliers.The paper is divided into six parts, the first part is introduction, itmainly gives the summary of outliers in regression analysis; the secondpart mainly introduces the definition of outliers,classification and kindsof outliers and the influence on the results of the regression analysis whenoutliers appear; the third part mainly discusses the applicability andproblems of the diagnosis and treatment methods in regression analysis;in the fourth part the efficiency of outliers diagnostics used commonly arebe compared by simulating different outliers in simple regression modeland multiple regression model. Part V gives a real case and its analysis.Finally, the conclusion, Innovation and future work will be presented.