TY - JOUR
T1 - Computational and statistical analyses for robust non-convex sparse regularized regression problem
AU - Katayama, Shota
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 15K15946 .
PY - 2019/7
Y1 - 2019/7
N2 - A robust and sparse estimation technique for linear regression problem is studied in this paper. Standard regression with Lasso, SCAD and MCP regularizations is not robust against outliers since it involves the least squares. To handle outliers, a two-stage procedure is proposed; at the first stage an initial estimator is calculated and then it is improved at the second stage by iteratively solving a sparse regression problem with reducing outlier effects. This procedure includes not only a random error but also a computational error. The convergence performance for the final estimator is investigated in both computational and statistical perspectives.
AB - A robust and sparse estimation technique for linear regression problem is studied in this paper. Standard regression with Lasso, SCAD and MCP regularizations is not robust against outliers since it involves the least squares. To handle outliers, a two-stage procedure is proposed; at the first stage an initial estimator is calculated and then it is improved at the second stage by iteratively solving a sparse regression problem with reducing outlier effects. This procedure includes not only a random error but also a computational error. The convergence performance for the final estimator is investigated in both computational and statistical perspectives.
KW - Computational and statistical analyses
KW - Robust estimation
KW - Sparse regularized regression
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U2 - 10.1016/j.jspi.2018.11.001
DO - 10.1016/j.jspi.2018.11.001
M3 - Article
AN - SCOPUS:85057571572
VL - 201
SP - 20
EP - 31
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
ER -