References
- Cai, Z., and H. Xiong. 2012. Partially varying coefficient instrumental variables models. Statistica Neerlandica 66 (2):85–110. doi: 10.1111/j.1467-9574.2011.00497.x.
- Cai, Z., Y. Fang, M. Lin, and J. Su. 2019. Inferences for a partially varying coefficient model with endogenous regressors. Journal of Business & Economic Statistics 37 (1):158–70. doi: 10.1080/07350015.2017.1294079.
- Card, D. 1993. Using geographic variation in college proximity to estimate the return to schooling (Technical Report). National Bureau of Economic Research. Cambridge, MA: NBER.
- 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.
- Greenland, S. 2000. An introduction to instrumental variables for epidemiologists. International Journal of Epidemiology 29 (4):722–9. doi: 10.1093/ije/29.4.722.
- Hernán, M. A., and J. M. Robins. 2006. Instruments for causal inference: An epidemiologist’s dream? Epidemiology (Cambridge, Mass.) 17 (4):360–72. doi: 10.1097/01.ede.0000222409.00878.37.
- Huang, J., and P. Zhao. 2018. Orthogonal weighted empirical likelihood-based variable selection for semiparametric instrumental variable models. Communications in Statistics-Theory and Methods 47 (18):4375–88. doi: 10.1080/03610926.2017.1373821.
- Huang, J., and P. Zhao. 2019. Instrumental variable based variable selection for generalized linear models with endogenous covariates. Communications in Statistics-Simulation and Computation 48 (6):1891–900. doi: 10.1080/03610918.2018.1425445.
- Huang, J., P. Zhao, and X. Huang. 2019. Instrumental variable based see variable selection for poisson regression models with endogenous covariates. Journal of Applied Mathematics and Computing 59 (1-2):163–78. doi: 10.1007/s12190-018-1173-0.
- Li, J., S. Ray, and B. G. Lindsay. 2007. A nonparametric statistical approach to clustering via mode identification. Journal of Machine Learning Research 8 (8):1687–723.
- Liu, C., P. Zhao, and Y. Yang. 2021. Regularization statistical inferences for partially linear models with high dimensional endogenous covariates. Journal of the Korean Statistical Society 50 (1):163–84. doi: 10.1007/s42952-020-00067-4.
- Lv, J., H. Yang, and C. Guo. 2017. Variable selection in partially linear additive models for modal regression. Communications in Statistics-Simulation and Computation 46 (7):5646–65. doi: 10.1080/03610918.2016.1171346.
- Schumaker, L. 2007. Spline functions: Basic theory. Cambridge, UK: Cambridge University Press.
- Tang, X., P. Zhao, Y. Yang, and W. Yang. 2022. Adjusted empirical likelihood inferences for varying coefficient partially non linear models with endogenous covariates. Communications in Statistics-Theory and Methods 51 (4):953–73. doi: 10.1080/03610926.2020.1747078.
- Yang, H., and J. Yang. 2014. A robust and efficient estimation and variable selection method for partially linear single-index models. Journal of Multivariate Analysis 129:227–42. doi: 10.1016/j.jmva.2014.04.024.
- Yang, H., J. Lv, and C. Guo. 2016. Robust estimation and variable selection for varying-coefficient single-index models based on modal regression. Communications in Statistics-Theory and Methods 45 (14):4048–67. doi: 10.1080/03610926.2014.915043.
- Yang, Y., L. Chen, and P. Zhao. 2017. Empirical likelihood inference in partially linear single-index models with endogenous covariates. Communications in Statistics-Theory and Methods 46 (7):3297–307. doi: 10.1080/03610926.2015.1060341.
- Yao, W., and L. Li. 2014. A new regression model: Modal linear regression. Scandinavian Journal of Statistics 41 (3):656–71. doi: 10.1111/sjos.12054.
- Yao, W., B. G. Lindsay, and R. Li. 2012. Local modal regression. Journal of Nonparametric Statistics 24 (3):647–63. doi: 10.1080/10485252.2012.678848.
- Yu, P., Z. Zhu, J. Shi, and X. Ai. 2020. Robust estimation for partial functional linear regression model based on modal regression. Journal of Systems Science and Complexity 33 (2):527–44. doi: 10.1007/s11424-020-8217-x.
- Yuan, J., P. Zhao, and W. Zhang. 2016. Semiparametric variable selection for partially varying coefficient models with endogenous variables. Computational Statistics 31 (2):693–707. doi: 10.1007/s00180-015-0601-y.
- Zhao, P., and G. Li. 2013. Modified see variable selection for varying coefficient instrumental variable models. Statistical Methodology 12:60–70. doi: 10.1016/j.stamet.2012.11.003.
- Zhao, P., and L. Xue. 2013. Empirical likelihood inferences for semiparametric instrumental variable models. Journal of Applied Mathematics and Computing 43 (1-2):75–90. doi: 10.1007/s12190-013-0652-6.
- Zhao, P., X. Zhou, X. Wang, and X. Huang. 2020. A new orthogonality empirical likelihood for varying coefficient partially linear instrumental variable models with longitudinal data. Communications in Statistics-Simulation and Computation 49 (12):3328–44. doi: 10.1080/03610918.2018.1547396.
- Zhao, W., R. Zhang, J. Liu, and Y. Lv. 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 (1):165–91. doi: 10.1007/s10463-013-0410-4.