Study On Robust Estimation And Outlier Detection Based On Multiple Linear Regression

In linear regression analysis,If outliers occur in the sample,it will affect the model establishment,parameter estimation and prediction.Therefore,the study of outliers in regression analysis has always been hotpot issue in statistics.In the traditional method of detecting outliers,the method of estimating the overall parameters in general is the least-squares method.However,the least-squares method is easily affected by the outliers,and the estimated results are not robust.Therefore,this paper introduced a robust estimate of the overall parameters when detecting outliers,making detection of outliers more efficient.Based on the linear regression model,based on the theory of mean shift model and data deletion model,This paper introduced a D statistic from the perspective of sum of squares of residuals,combined the M-estimate,R-estimate,sample quantile method,LMS-estimate,LTS-estimate and S-estimate to estimate robust overall parameters,to improve the D statistic,and finally used the improved D statistic to judge whether the observed value is an outlier and estimated its size.By simulation experiments with the large amount of data and experiments with real data,the improved D statistics and traditional methods for detecting outliers was compared.The main work of this paper was as follows:(1)Some robust estimation methods based on multiple linear regression were studied.(2)Based on the data deletion model and mean shift model,a statistic for detecting outliers was introduced,and robust estimation was combined.(3)Using R,Python and other software to carry out simulation experiments with the large amount of data and experiments with real data,the new method of detecting outliers was compared with the traditional method of detecting outliers.