Variable selection in partially linear additive models for modal regression

References

• de Boor, C. (2001). A Practical Guide to Splines. New York: Springer.
   Google Scholar
• Dielman, T. E. (2005). Least absolute value regression: Recent contributions. Journal of Statistical Computation and Simulation 75:263–286.
   Google Scholar
• Du, P., Cheng, G., Liang, H. (2012). Semiparametric regression models with additive nonparametric components and high dimensional parametric components. Computational Statistics and Data Analysis 56:2006–2017.
   Google Scholar
• Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96:1348–1360.
   Google Scholar
• Guo, J., Tang, M., Tian, M., Zhu, K. (2013). Variable selection in high-dimensional partially linear additive models for composite quantile regression. Computational Statistics and Data Analysis 66:56–67.
   Google Scholar
• Härdle, W., Liang, H., Gao, J. (2000). Partially Linear Models. Heidelberg: Springer Physica.
   Google Scholar
• Härdle, W. K., Müller, M., Sperlich, S., Werwatz, A. (2004). Nonparametric and Semiparametric Models. New York: Springer-Verlag.
   Google Scholar
• Koenker, R. (2005). Quantile Regression. Cambridge: Cambridge University Press.
   Google Scholar
• Li, J., Ray, S., Lindsay, B. (2007). A nonparametric statistical approach to clustering via mode identification. Journal of Machine Learning Research 8:1687–1723.
   Google Scholar
• Lian, H. (2012). Variable selection in high-dimensional partly linear additive models. Journal of Nonparametric Statistics 24:825–839.
   Google Scholar
• Liu, X., Wang, L., Liang, H. (2011). Variable selection and estimation for semiparametric additive partial linear models. Statistica Sinica 21:1225–1248.
   Google Scholar
• Liu, J., Zhang, R., Zhao, W., Lv, Y. (2013). A robust and efficient estimation method for single index models. Journal of Multivariate Analysis 122:226–238.
   Google Scholar
• Lv, Z., Zhu, H., Yu, K. (2014). Robust variable selection for nonlinear models with diverging number of parameters. Statistics and Probability Letters 91:90–97.
   Google Scholar
• Ma, S., Yang, L. (2011). Spline-backfitted kernel smoothing of partially linear additive model. Journal of Statistical Planning and Inference 141:204–219.
   Google Scholar
• Schumaker, L. (1981). Spline Functions: Basic Theory. New York: Wiley.
   Google Scholar
• Wang, H., Xia, Y. (2009). Shrinkage estimation of the varying coefficient model. Journal of the American Statistical Association 104:747–757.
   Google Scholar
• Wang, L., Liu, X., Liang, H., Carroll, R. J. (2011). Estimation and variable selection for generalized additive partial linear models. The Annals of Statistics 39:1827–1851.
   Google Scholar
• Yang, H., Guo, C., Lv, J. (2014). A robust and efficient estimation method for single-index varying-coefficient models. Statistics and Probability Letters 94:119–127.
   Google Scholar
• Yao, W. (2013). A note on EM algorithm for mixture models. Statistics and Probability Letters 83:519–526.
   Google Scholar
• Yao, W., Li, L. (2014). A new regression model: Modal linear regression. Scandinavian Journal of Statistics 41:656–671.
   Google Scholar
• Yao, W., Lindsay, B., Li, R. (2012). Local modal regression. Journal of Nonparametric Statistics 24:647–663.
   Google Scholar
• Zhao, W., Zhang, R., Liu, J., Lv, Y. (2014). Robust and efficient variable selection for semiparametric partially linear varying coefficient model based on modal regression. Annals of the Institute of Statistical Mathematics 66:165–191.
   Google Scholar
• Zhu, H., Lv, Z., Yu, K., Deng, C. (2015). Robust variable selection in partially varying coefficient single-index model. Journal of the Korean Statistical Society 44:45–57.
   Google Scholar
• Zou, H., Yuan, M. (2008). Composite quantile regression and the oracle model selection theory. The Annals of Statistics 36:1108–1126.
   Google Scholar