Research On Robust Regression And Outlier Detection Based On Non-convex Penalty Likelihood Method

The least square estimation is to find the best parameter estimation by minimizing the sum of squares of residuals,which is most commonly used and can get a satisfying result.However,outliers are common in the real data,so the least square regression is not accurate for statistical analysis.Even if there is only one outlier,it will negatively affect the accuracy of the estimation.The robust regression which can achieve high breakdown point and high efficiency shows practical significance.This paper introduces a new method based on penalized regression,which add a mean shift parameter in linear regression model,and the regularization method is used to sparse the parameter.By testing,the non-convex penalty can do better in dealing with the high leverage outliers.We can identify outliers by checking whether the mean shift parameter is non-zero.Then,subtract the mean shift parameter from the dependent variable,and use the least square regression to get the estimation of the regression parameter.We use M,S and JD to evaluate the performance of each method in identifying outliers,and use the mean square parameter error to evaluate the goodness-of-fit of the model.By comparing the robust regression method based on non-convex penalty likelihood with REWLSE and MM-estimation,we found that the robust regression based on non-convex penalty likelihood has better robustness and outlier detection ability,and the breakdown point is higher.It can solve the problem that the commonly used robust regression method is ineffective when one or more high leverage outliers exist,and obtain more reliable results in the simulation test.At the same time,the existing problems of this new method are also discussed.In this paper,the empirical breakdown points and validity of the robust regression method based on penalty likelihood will be measured preliminarily,and the method will be further improved.In this paper,we also try to combine robust Mahalanobis distance with the residuals of REWLSE and MM-estimation to detect outliers.It is found that this method performs better in the swamping,and this method can correct a small part of error identification of the estimation itself,and the breakdown point is slightly higher.