Ultrahigh dimensional single index model estimation via refitted cross-validation

References

• Altham, P. M. E. 1984. Improving the precision of estimation by fitting a model. Journal of the Royal Statistical Society. Series B (Methodological) 46 (1):118–9. doi: 10.1111/j.2517-6161.1984.tb01283.x.
   Google Scholar
• Carroll, R. J., J. Fan, I. Gijbels, and M. P. Wand. 1997. Generalized partially linear single-index models. Journal of the American Statistical Association 92 (438):477–89. doi: 10.1080/01621459.1997.10474001.
   Web of Science ®Google Scholar
• Chen, Z., Fan, J., and R. Li. 2018. Error variance estimation in ultrahigh-dimensional additive models. Journal of the American Statistical Association 113 (521):315–27. doi: 10.1080/01621459.2016.1251440.
   PubMed Web of Science ®Google Scholar
• De Boor, C. 2001. A pactical guide to splines, vol. 27. New York: Springer-Verlag.
   Google Scholar
• DeVore, R. A., and G. G. Lorentz. 1993. Constructive approximation, vol. 303., New York, Berlin: Springer-Verlag.
   Google Scholar
• Fan, J., Y. Feng, and R. Song. 2011. Nonparametric independence screening in sparse ultra-high-dimensional additive models. Journal of the American Statistical Association 106 (494):544–57. doi: 10.1198/jasa.2011.tm09779.
   PubMed Web of Science ®Google Scholar
• Fan, J., S. Guo, and N. Hao. 2012. Variance estimation using refitted cross-validation in ultrahigh dimensional regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 74 (1):37–65. doi: 10.1111/j.1467-9868.2011.01005.x.
   PubMed Web of Science ®Google Scholar
• Fan, J., and R. Li, 2001. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96 (456):1348–60. doi: 10.1198/016214501753382273.
   Web of Science ®Google Scholar
• Fan, J., and J. Lv. 2008. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 70 (5):849–911. doi: 10.1111/j.1467-9868.2008.00674.x.
   PubMed Web of Science ®Google Scholar
• Fan, J., Y. Ma, and W. Dai. 2014. Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models. Journal of the American Statistical Association 109 (507):1270–84. doi: 10.1080/01621459.2013.879828.
   PubMed Web of Science ®Google Scholar
• Fan, J. and H. Peng. 2004. Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics 32 (3):928–61. doi: 10.1214/009053604000000256.
   Web of Science ®Google Scholar
• Fan, J., R. Samworth, and Y. Wu. 2009. Ultrahigh dimensional feature selection: Beyond the linear model. The Journal of Machine Learning Research 10:2013–38.
   PubMed Web of Science ®Google Scholar
• Hardle, W. and T. M. Stoker. 1989. Investigating smooth multiple regression by the method of average derivatives. Journal of the American Statistical Association 84 (408):986–95. doi: 10.2307/2290074.
   Web of Science ®Google Scholar
• Hristache, M., A. Juditsky, and V. Spokoiny. 2001. Direct estimation of the index coefficient in a single-index model. Annals of Statistics 29 (3):595–623.
   Web of Science ®Google Scholar
• Huang, J. Z. 2003. Local asymptotics for polynomial spline regression. The Annals of Statistics 31 (5):1600–35. doi: 10.1214/aos/1065705120.
   Web of Science ®Google Scholar
• Ichimura, H. 1993. Semiparametric least squares (sls) and weighted sls estimation of single-index models. Journal of Econometrics 58 (1-2):71–120. doi: 10.1016/0304-4076(93)90114-K.
   Web of Science ®Google Scholar
• Li, K.-C. 1991. Sliced inverse regression for dimension reduction. Journal of the American Statistical Association 86 (414):316–27. doi: 10.1080/01621459.1991.10475035.
   Web of Science ®Google Scholar
• Li, R., W. Zhong, and L. Zhu. 2012. Feature screening via distance correlation learning. Journal of the American Statistical Association 107 (499):1129–39. doi: 10.1080/01621459.2012.695654.
   PubMed Web of Science ®Google Scholar
• Liu, J., R. Li, and R. Wu. 2014. Feature selection for varying coefficient models with ultrahigh-dimensional covariates. Journal of the American Statistical Association 109 (505):266–74. doi: 10.1080/01621459.2013.850086.
   PubMed Web of Science ®Google Scholar
• Liu, J., W. Zhong, and R. Li. 2015. A selective overview of feature screening for ultrahigh-dimensional data. Science China Mathematics 58 (10):1–22. doi: 10.1007/s11425-015-5062-9.
   Web of Science ®Google Scholar
• Peng, H., and T. Huang. 2011. Penalized least squares for single index models. Journal of Statistical Planning and Inference 141 (4):1362–79. doi: 10.1016/j.jspi.2010.10.003.
   Web of Science ®Google Scholar
• Powell, J. L., J. H. Stock, and T. M. Stoker. 1989. Semiparametric estimation of index coefficients. Econometrica 57 (6):1403–30. doi: 10.2307/1913713.
   Web of Science ®Google Scholar
• Schumaker, L. 2007. Spline functions: Basic theory. New York: Cambridge University Press.
   Google Scholar
• Tibshirani, R. 2011. Regression shrinkage and selection via the lasso: a retrospective. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 73 (3):273–82. doi: 10.1111/j.1467-9868.2011.00771.x.
   Web of Science ®Google Scholar
• Wang, G., and L. Wang. 2015. Spline estimation and variable selection for single-index prediction models with diverging number of index parameters. Journal of Statistical Planning and Inference 162:1–19. doi: 10.1016/j.jspi.2015.01.007.
   Web of Science ®Google Scholar
• Wang, L., Z. Chen, C. D. Wang, and R. Li. 2020. Ultrahigh dimensional precision matrix estimation via refitted cross validation. Journal of econometrics 215 (1):118–30. doi: 10.1016/j.jeconom.2019.08.004.
   PubMed Web of Science ®Google Scholar
• Wang, L., J. Liu, Y. Li, and R. Li. 2017. Model-free conditional independence feature screening for ultrahigh dimensional data. Science China Mathematics 60 (3):551–68. doi: 10.1007/s11425-016-0186-8.
   PubMed Web of Science ®Google Scholar
• Wang, L., and L. Yang. 2009. Spline estimation of single-index models. Statistica Sinica 19 (2):765–83.
   Web of Science ®Google Scholar
• Wang, Z., and L. Xue. 2019. Variance estimation for sparse ultra-high dimensional varying coefficient models. Communications in Statistics-Theory and Methods 48 (5):1270–83. doi: 10.1080/03610926.2018.1429627.
   Web of Science ®Google Scholar
• Xia, Y., and W. Härdle. 2006. Semi-parametric estimation of partially linear single-index models. Journal of Multivariate Analysis 97 (5):1162–84. doi: 10.1016/j.jmva.2005.11.005.
   Web of Science ®Google Scholar
• Xia, Y., and W. K. Li. 1999. On single-index coefficient regression models. Journal of the American Statistical Association 94 (448):1275–85. doi: 10.1080/01621459.1999.10473880.
   Web of Science ®Google Scholar
• Xia, Y., H. Tong, W. K. Li, and L.-X. Zhu. 2002. An adaptive estimation of dimension reduction space. Journal of the Royal Statistical Society. Series B (Statistical Methodology) 64 (3):363–410. doi: 10.1111/1467-9868.03411.
   Web of Science ®Google Scholar
• Yu, Y., and D. Ruppert. 2002. Penalized spline estimation for partially linear single-index models. Journal of the American Statistical Association 97 (460):1042–54. doi: 10.1198/016214502388618861.
   Web of Science ®Google Scholar
• Zhang, C.-H. 2010. Nearly unbiased variable selection under minimax concave penalty. The Annals of statistics 38 (2):894–942. doi: 10.1214/09-AOS729.
   Web of Science ®Google Scholar
• Zhong, W., L. Zhu, R. Li, and H. Cui. 2016. Regularized quantile regression and robust feature screening for single index models. Statistica Sinica 26 (1):69–95. doi: 10.5705/ss.2014.049.
   PubMed Web of Science ®Google Scholar
• Zhou, S., X. Shen, D. Wolfe. 1998. Local asymptotics for regression splines and confidence regions. The Annals of Statistics 26 (5):1760–82 doi: 10.1214/aos/1024691356.
   Web of Science ®Google Scholar
• Zhu, L.-P., L. Li, R. Li, and L.-X. Zhu. 2011a. Model-free feature screening for ultrahigh-dimensional data. Journal of the American Statistical Association 106 (496):1464–75. doi: 10.1198/jasa.2011.tm10563.
   PubMed Web of Science ®Google Scholar
• Zhu, L.-P., L.-Y. Qian, and J.-G. Lin. 2011b. Variable selection in a class of single-index models. Annals of the Institute of Statistical Mathematics 63 (6):1277–93. doi: 10.1007/s10463-010-0287-4.
   Web of Science ®Google Scholar