Communications for Statistical Applications and Methods

  • 제15권5호
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  • Pages.753-764
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  • 2008
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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The Doubly Regularized Quantile Regression

  • Choi, Ho-Sik (Department of Informational Statistics and Institute of Basic Science, Hoseo University) ;
  • Kim, Yong-Dai (Department of Statistics, Seoul National University)
  • 발행 : 2008.09.30
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초록

The $L_1$ regularized estimator in quantile problems conduct parameter estimation and model selection simultaneously and have been shown to enjoy nice performance. However, $L_1$ regularized estimator has a drawback: when there are several highly correlated variables, it tends to pick only a few of them. To make up for it, the proposed method adopts doubly regularized framework with the mixture of $L_1$ and $L_2$ norms. As a result, the proposed method can select significant variables and encourage the highly correlated variables to be selected together. One of the most appealing features of the new algorithm is to construct the entire solution path of doubly regularized quantile estimator. From simulations and real data analysis, we investigate its performance.

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참고문헌

  1. Choi, H. (2007). An extension of COSSO algorithm by combining variables, Journal of the Korean Data Analysis Society, 9, 2117-2125
  2. Efron, B., Hastie, T., Johnstone, I. and Tibshirani, R. (2004). Least angle regression, The Annals of Statistics, 32, 407-499 https://doi.org/10.1214/009053604000000067
  3. Huang, J., Ma, S. and Zhang, C. H. (2006). Adaptive Lasso for sparse high-dimensional regression models, Technical Paper 374, University of Iowa, Dept. of Statistics and Actuarial Science
  4. Koenker, R. and Bassett, G. (1978). Regression quantiles, Econometrica, 46, 33-50 https://doi.org/10.2307/1913643
  5. Koenker, R., Ng, P. and Portnoy, S. (1994). Quantile smoothing splines, Biometrika, 81, 673-680 https://doi.org/10.1093/biomet/81.4.673
  6. Li, Y., Liu, Y. and Zhu, J. (2007). Quantile regression in reproducing kernel Hilbert spaces, Journal of the American Statistical Association, 102, 255-268 https://doi.org/10.1198/016214506000000979
  7. Li, Y. and Zhu, J. (2008). $L_1$-norm Quantile Regression, Journal of Computational & Graphical Statistics, 17, 163-185 https://doi.org/10.1198/106186008X289155
  8. Oh, H. S., Nychka, D., Brown, T. and Charbonneau, P. (2004). Period analysis of variable stars by robust smoothing, Journal of the Royal Statistical Society, Series C, 53, 15-30 https://doi.org/10.1111/j.1467-9876.2004.00423.x
  9. Scheetz, T. E., Kim, K. Y., Swiderski, R. E., Philp, A. R., Braun, T. A., Knudtson, K. L., Dorrance, A. M., DiBona, G. F., Huang, J., Casavant, T. L., Sheffield, V. C. and Stone, E. M. (2006). Regulation of gene expression in the mammalian eye and its relevance to eye disease, Proceedings of the National Academy of Sciences, 103, 14429-14434
  10. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society, Series B, 58, 267-288
  11. Wang, L., Zhu, J. and Zou, H. (2006). The doubly regularized support vector machine, Statistica Sinica, 16, 589-615
  12. Yuan, M. (2006). GACV for quantile smoothing splines, Computational Statistics & Data Analysis, 50, 813-829 https://doi.org/10.1016/j.csda.2004.10.008
  13. Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net, Journal of Royal Statistical Society, Series B, 67, 301-320 https://doi.org/10.1111/j.1467-9868.2005.00503.x