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Parameter Estimation And Empirical Breakdown Point Of Robust Mixture Regression Model

Posted on:2021-04-02Degree:MasterType:Thesis
Country:ChinaCandidate:X W XiongFull Text:PDF
GTID:2427330629988215Subject:Applied Statistics
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Mixture regression model has been widely used in various heterogeneous data,and most of them are estimated by EM calculation based on MLE.When there are outliers,the defects and unsteadiness of MLE algorithm are highlighted.For this reason,many robust hybrid regression models have been developed,such as TLE,M-estimation,tdistribution-based robust hybrid regression model.There are only mixture regression models based on L0 penalty function and L1 penalty function.This paper proposes SCAD based mixture regression model and hard ridge based mixture regression model and explores their robustness.Based on swamping(s),masking(m),joint detection(JD),and other aspects,this paper explores the advantages and disadvantages of each of the above-mentioned robust mixture regression models,and further explores the effect of different penalty functions such as(SCAD,hard ridge)combined with RM2 robust mixture regression model.Finally,we explore the collapse points of different robust regression models(when the proportion of outliers,especially the strong leverage point reaches,when the model is no longer robust)and their different practical ranges.The results are as follows:(1)When the x-axis and y-axis have abnormal points,the collapse points of different robust mixture regression models are different,among which the highest is based on SCAD penalty function,and the lowest is based on MEMbisquare.(2)In the case of 20% outliers,all the robust mixture regression models are robust.(3)The robust mixture regression model based on SCAD penalty function is the most robust when the residual of data is based on t-distribution.(4)In the case of 20 "bad" high leverage points,the robust mixture regression model based on SCAD penalty function is still the most robust.All the above simulation experiments prove that the robust mixture regression model based on SCAD penalty function is robust.
Keywords/Search Tags:SCAD, Robust mixture regression model, TLE, bi-square, t-distribution
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