I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surpr...I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.展开更多
When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot ...When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.展开更多
文摘I first met Constantine Dafermos in August 1974, at a meeting at Brown University, where I was invited because my former advisor （Jacques-Louis LIONS） could not come, and he had proposed my name. I was happily surprised that Constantine greeted me as if he knew me well, and since for many years now I have considered him as if he was an older brother, I wonder when this feeling started.
基金supported by the National Natural Science Foundation of China under Grant Nos.12271294,12171225 and 12071248.
文摘When there are outliers or heavy-tailed distributions in the data, the traditional least squares with penalty function is no longer applicable. In addition, with the rapid development of science and technology, a lot of data, enjoying high dimension, strong correlation and redundancy, has been generated in real life. So it is necessary to find an effective variable selection method for dealing with collinearity based on the robust method. This paper proposes a penalized M-estimation method based on standard error adjusted adaptive elastic-net, which uses M-estimators and the corresponding standard errors as weights. The consistency and asymptotic normality of this method are proved theoretically. For the regularization in high-dimensional space, the authors use the multi-step adaptive elastic-net to reduce the dimension to a relatively large scale which is less than the sample size, and then use the proposed method to select variables and estimate parameters. Finally, the authors carry out simulation studies and two real data analysis to examine the finite sample performance of the proposed method. The results show that the proposed method has some advantages over other commonly used methods.
