Robust Statistical Methods in Variable Selection

다국어 초록 (Multilingual Abstract)

Variable selection is an important research field in linear regression modeling with high-dimensional predictors. We proposed a robust penalized regression estimator which provides automatically selection of variables and estimation of regression parameters together. It is based on the least absolute deviation and the non-convex penalty function, the smoothly clipped absolute deviation suggested by Fan and Li(2001). We developed the algorithm for the proposed estimator using the local quadratic approximation and chose the tuning parameter of the penalty function. The algorithm needs only linear equations and so we can obtain quickly the estimators. The simulation result shows that the proposed estimator is robust and efficient for non-normal cases.

참고문헌 (Reference)

1 Fan, J., "Variable selection via nonconcave penalized likelihood and its oracle properties" 96 : 1348-1360, 2001

2 Wang, H., "Tuning parameter selectors for the smoothly clipped absolute deviation method" 94 : 553-568, 2007

3 Hastie, T., "The Elements of Statistical Learning: Data Mining, Inference, and Prediction" Springer 2001

4 Wang, H., "Robust regression shrinkage and consistent variable selection through the LAD-Lasso" 25 : 347-355, 2007

5 Huber, P. J., "Robust Statistics" John Wiley and Sons. 1981

6 Rousseeuw, P. J., "Robust Regression and Outlier Detection" John Wiley. 1987

7 Tibshirani, R. J., "Regression shrinkage and selection via the LASSO" 58 : 267-288, 1996

8 Akaike, H., "Information theory and an extension of the maximum likelihood principle" 267-281, 1973

9 Zhang, H. H., "Gene selection using support vector machines with non-convex penalty" 22 : 88-95, 2006

10 Kittler, J., "Feature selection and extraction, In: Handbook of Pattern Recognition and Image Processing" Academic Press 1986

11 Schwarz, G., "Estimating the dimension of a model" 6 : 461-464, 1978

12 김명근, "Distance Measures in Multivariate Constrained Regression" 한국자료분석학회 10 (10): 693-700, 2008

13 김명근, "Detection of Outliers in Multivariate Regression Using Plug-in Method" 한국자료분석학회 7 (7): 1117-1124, 2005

14 Leng, C., "A note on the LASSO and related procedures in model selection" 16 : 1273-1284, 2006

15 정강모, "A Robust Estimator in Ridge Regression" 한국자료분석학회 9 (9): 535-543, 2007

16 정강모, "A Detection Method of Multivariate Outliers using Decompositions of the Squared Mahalanobis Distance" 한국자료분석학회 7 (7): 1935-1943, 2005