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Moderately clipped LASSO

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  • Kwon, Sunghoon
  • Lee, Sangin
  • Kim, Yongdai

Abstract

The least absolute shrinkage and selection operator (LASSO) has been widely used in high-dimensional linear regression models. However, it is known that the LASSO selects too many noisy variables. In this paper, we propose a new estimator, the moderately clipped LASSO (MCL), that deletes noisy variables successively without sacrificing prediction accuracy much. Various numerical studies are done to illustrate superiority of the MCL over other competitors.

Suggested Citation

  • Kwon, Sunghoon & Lee, Sangin & Kim, Yongdai, 2015. "Moderately clipped LASSO," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 53-67.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:53-67
    DOI: 10.1016/j.csda.2015.07.001
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Yuhong Yang, 2005. "Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation," Biometrika, Biometrika Trust, vol. 92(4), pages 937-950, December.
    3. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    4. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    5. Yongdai Kim & Sunghoon Kwon, 2012. "Global optimality of nonconvex penalized estimators," Biometrika, Biometrika Trust, vol. 99(2), pages 315-325.
    6. Kim, Yongdai & Choi, Hosik & Oh, Hee-Seok, 2008. "Smoothly Clipped Absolute Deviation on High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1665-1673.
    7. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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    Cited by:

    1. Yang Peng & Bin Luo & Xiaoli Gao, 2022. "Robust Moderately Clipped LASSO for Simultaneous Outlier Detection and Variable Selection," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 694-707, November.
    2. Sunghoon Kwon & Jeongyoun Ahn & Woncheol Jang & Sangin Lee & Yongdai Kim, 2017. "A doubly sparse approach for group variable selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 997-1025, October.
    3. Joaquim Fernando Pinto da Costa & Manuel Cabral, 2022. "Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works," Mathematics, MDPI, vol. 10(6), pages 1-22, March.

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