Robust Estimators Of Regression Parameters And Covariance Matrix

We have witnessed a great success on L2 cost function? y-X??22 in linear regression,.But it is sensitive to outliers.L1 cost function? y-X??1is much more robust.In the past several dacades,it is not popular because of its compute complexity.But recent years,its algorithm has made a breakthrough.This thesis proposes a new method which combines the both advantages,avoids both weak-nesses.The new method introduces a new parameter ?.We can choose different values for different samples,which gives us much flexibility.Simulation shows that the proposed method is much robust.Mean while,it speed is also fast.Then this method is generalized into high dimensional data.The second part of the thesis contains chapter 4 and chapter 5,focuses on the robust estimator of the covariance matrix.I generalize the sample covariance matrix S by introduce a new parameter a.The new estimator is much more robust which can be controlled by ?.Then I try to use this method in high dimensional data by shrinkage it into unit matrix,chapter 5 gives the shrinkage coefficient.