Variable Screening via Quantile Partial Correlation

References

• Angrist, J. , Chernozhukov, V. , and Fernández-Val, I. (2006), “Quantile Regression Under Misspecification, With an Application to the U.S. Wage Structure,” Econometrika , 74, 539–563.
   Web of Science ®Google Scholar
• Belloni, A. , and Chernozhukov, V. (2011), “ ℓ1 -Penalized Quantile Regression in High-Dimensional Sparse Model,” Annals of Statistics , 95, 759–771.
   Google Scholar
• Bühlmann, P. , Kalisch, M. , and Maathuis, M. (2009), “Variable Selection for High-Dimensional Models: Partially Faithful Distributions and the PC-Simple Algorithm,” Biometrika , 97, 1–19.
   Web of Science ®Google Scholar
• Chen, J. , and Chen, Z. (2008), “Extended Bayesian Information Criteria for Model Selection With Large Model Spaces,” Biometrika , 95, 759–771.
   Web of Science ®Google Scholar
• Cho, H. , and Fryzlewicz, P. (2012), “High Dimensional Variable Selection via Tilting,” Journal of the Royal Statistical Society , Series B, 74, 593–622.
   Google Scholar
• Fan, J. , Feng, Y. , and Song, R. (2011), “Nonparametric Independence Screening in Sparse Ultra-High Dimensional Additive Models,” Journal of the American Statistical Association , 106, 544–557.
   PubMed Web of Science ®Google Scholar
• Fan, J. , and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties,” Journal of the American Statistical Association , 96, 1348–1360.
   Web of Science ®Google Scholar
• Fan, J. , and Lv, J. (2008), “Sure Independence Screening for Ultra-High Dimensional Feature Space” (with discussion), Journal of the Royal Statistical Society , Series B, 70, 849–911.
   Google Scholar
• ——— (2010), “A Selective Overview of Variable Selection in High Dimensional Feature Space,” Statistica Sinica , 20, 101–148.
   PubMed Web of Science ®Google Scholar
• ——— (2010), “Sure Independence Screening in Generalized Linear Models with NP-Dimensionality,” The Annals of Statistics , 38, 3567–3604.
   Web of Science ®Google Scholar
• He, X. , Wang, L. , and Hong, H. G. (2013), “Quantile-Adaptive Model-Free Variable Screening for High-Dimensional Heterogeneous Data,” Annals of Statistics , 41, 342–369.
   Web of Science ®Google Scholar
• Huang, J. , Horowitz, J. L. , and Ma, S. (2008b), “Asymptotic Properties of Bridge Estimators in Sparse High-Dimensional Regression Models,” Annals of Statistics , 36, 587–613.
   Web of Science ®Google Scholar
• Huang, J. , Ma, S. G. , and Zhang, C. H. (2008a), “Adaptive Lasso for Sparse High-Dimensional Regression Models,” Statistica Sinica , 18, 1603–1618.
   Web of Science ®Google Scholar
• Kalisch, M. , and Bühlmann, P. (2007), “Estimating High-Dimensional Directed Acyclic Graphs With the PC-Algorithm,” Journal of Machine Learning Research , 8, 613–636.
   Web of Science ®Google Scholar
• Koenker, R. (2005), Quantile Regression , New York: Cambridge University Press.
   Google Scholar
• Kutner, M. H. , Nachtsheim, C. J. , Neter, J. , and Li, W. (2005), Applied Linear Statistical Models (5th ed.), New York: McGraw-Hill and Irwin.
   Google Scholar
• Lee, E. R. , Noh, H. , and Park, B. U. (2014), “Model Selection via Bayesian Information Criterion for Quantile Regression Models,” Journal of the American Statistical Association , 109, 216–229.
   Web of Science ®Google Scholar
• Li, G. , Li, Y. , and Tsai, C. L. (2015), “Quantile Correlations and Quantile Autoregressive Modeling,” Journal of the American Statistical Association , 110, 246–261.
   Web of Science ®Google Scholar
• Li, R. , Zhong, W. , and Zhu, L. (2012), “Feature Screening via Distance Correlation Learning,” Journal of American Statistical Association , 107, 1129–1139.
   PubMed Web of Science ®Google Scholar
• Liu, J. , Li, R. , and Wu, R. (2014), “Feature Selection for Varying Coefficient Models With Ultrahigh Dimensional Covariates,” Journal of the American Statistical Association , 109, 266–274.
   PubMed Web of Science ®Google Scholar
• Nagelkerke, N. J. D. (1991), “A Note on a General Definition of the Coefficient of Determination,” Biometrika , 78, 691–692.
   Web of Science ®Google Scholar
• Scheetz, T. E. , Kim, K.-Y. A. , 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 of the United States of America , 103, 14429–14434.
   PubMed Web of Science ®Google Scholar
• Schwarz, C. (1978), “Estimating the Dimension of a Model,” The Annals of Statistics , 6, 461–464.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection via the LASSO,” Journal of the Royal Statistical Society , Series B, 58, 267–288.
   Google Scholar
• Wang, H. (2009), “Forward Regression for Ultra-High Dimensional Variable Screening,” Journal of the American Statistical Association , 104, 1512–1524.
   Web of Science ®Google Scholar
• Wang, H. , Li, B. , and Leng, C. (2009), “Shrinkage Tuning Parameter Selection With a Diverging Number of Parameters,” Journal of Royal Statistical Society , Series B, 71, 671–683.
   Google Scholar
• Wang, H. , Li, R. , and Tsai, C.-L. (2007), “Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method,” Biometrika , 94, 553–568.
   PubMed Web of Science ®Google Scholar
• Wang, L. , Wu, Y. , and Li, R. (2012), “Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension,” Journal of the American Statistical Association , 107, 214–222.
   PubMed Web of Science ®Google Scholar
• Wu, Y. , and Yin, G. (2015), “Conditional Quantile Screening in Ultrahigh-Dimensional Heterogeneous Data,” Biometrika , 102, 65–76.
   Web of Science ®Google Scholar
• Zhang, C. H. (2010), “Nearly Unbiased Variable Selection Under Minimax Concave Penalty,” The Annals of Statistics , 38, 894–942.
   Web of Science ®Google Scholar
• Zhu, L.-P. , Li, L. , Li, R. , and Zhu, L.-X. (2011), “Model-Free Feature Screening for Ultrahigh-Dimensional Data,” Journal of the American Statistical Association , 106, 1464–1475.
   PubMed Web of Science ®Google Scholar
• Zou, H. (2006), “The Adaptive Lasso and Its Oracle Properties,” Journal of the American Statistical Association , 101, 1418–1429.
   Web of Science ®Google Scholar
• Zou, H. , and Hastie, T. (2005), “Regression Shrinkage and Selection via the Elastic Net With Application to Microarrays,” Journal of the Royal Statistical Society , Series B, 67, 301–320.
   Google Scholar