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Articles

Double penalized regularization estimation for partially linear instrumental variable models with ultrahigh dimensional instrumental variables

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Pages 4636-4653 | Received 19 Dec 2020, Accepted 02 Aug 2021, Published online: 09 Sep 2021

References

  • Bai, Y., Z. Y. Zhu, and W. K. Fung. 2008. Partial linear models for longitudinal data based on quadratic inference functions. Scandinavian Journal of Statistics 35 (1):104–18. doi:10.1111/j.1467-9469.2007.00578.x.
  • Belloni, A., D. Chen, V. Chernozhukov, and C. Hansen. 2012. Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80 (6):2369–429.
  • Bound, J., D. A. Jaeger, and R. M. Baker. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogeneous explanatory variable is weak. Journal of the American Statistical Association 90 (430):443–50. doi:10.2307/2291055.
  • 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.
  • Card, D. 1995. Using geographic variation in college proximity to estimate the return to schooling. In Aspects of labor market behaviour: Essays in honour of John Vanderkamp, ed. L. Christofides, E. Grant, and R. Swidinsky, 201–22. Toronto: University of Toronto Press.
  • Chen, B. C., H. Liang, and Y. Zhou. 2016. GMM estimation in partial linear models with endogenous covariates causing an over-identified problem. Communications in Statistics - Theory and Methods 45 (11):3168–84. doi:10.1080/03610926.2014.901363.
  • Chen, C., M. Ren, M. Zhang, and D. B. Zhang. 2018. A Two-stage penalized least squares method for constructing large systems of structural equations. Journal of Machine Learning Research 19 (2):1–34.
  • Chernozhukov, V., and C. Hansen. 2008. The reduced form: A simple approach to inference with weak instruments. Economics Letters 100 (1):68–71. doi:10.1016/j.econlet.2007.11.012.
  • Didelez, V., S. Meng, and N. A. Sheehan. 2010. Assumptions of IV methods for observational epidemiology. Statistical Science 25 (1):22–40. doi:10.1214/09-STS316.
  • Fan, J. Q., 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.
  • Fan, J. Q., and R. Z. Li. 2004. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of the American Statistical Association 99 (467):710–23. doi:10.1198/016214504000001060.
  • Fan, J. Q., and J. C. Lv. 2008. Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society Series B 70:849–911. doi:10.1111/j.1467-9868.2008.00674.x.
  • Fan, J. Q., and Y. Liao. 2014. Endogeneity in High Dimensions. Annals of Statistics 42 (3):872–917. doi:10.1214/13-AOS1202.
  • 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.
  • Hernan, M. A., and J. M. Robins. 2006. Instruments for causal inference: An epidemiologist’s dream? Epidemiology 17 (4):360–72. doi:10.1097/01.ede.0000222409.00878.37.
  • Huang, J. T., and P. X. Zhao. 2017. QR decomposition based orthogonality estimation for partially linear models with longitudinal data. Journal of Computational and Applied Mathematics 321:406–15. doi:10.1016/j.cam.2017.02.024.
  • Huang, J. T., and P. X. 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.
  • Liang, H., and R. Li. 2009. Variable selection for partially linear models with measurement errors. Journal of the American Statistical Association 104 (485):234–48. doi:10.1198/jasa.2009.0127.
  • Lin, W., R. Feng, and H. Z. Li. 2015. Regularization methods for high-dimensional instrumental variables regression with an application to genetical genomics. Journal of the American Statistical Association 110 (509):270–88. doi:10.1080/01621459.2014.908125.
  • Liu, C. Q., P. X. Zhao, and Y. P. 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.
  • Liu, J. Y., L. J. Lou, and R. Z. Li. 2018. Variable selection for partially linear models via partial correlation. Journal of Multivariate Analysis 167:18–434. doi:10.1016/j.jmva.2018.06.005.
  • Massart, P. 2000. About the constants in Talagrand’s concentration inequalities for empirical processes. The Annals of Probability 28 (2):863–84. doi:10.1214/aop/1019160263.
  • Newhouse, J. P., and M. McClellan. 1998. Econometrics in outcomes research: The use of instrumental variables. Annual Review of Public Health 19 (1):17–24. doi:10.1146/annurev.publhealth.19.1.17.
  • Schumaker, L. L. 1981. Spline function. New York: Wiley.
  • Tibshirani, R. 1996. Regression shrinkage and selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58 (1):267–88. doi:10.1111/j.2517-6161.1996.tb02080.x.
  • Vaart, A., and J. A. Wellner. 1996. Weak convergence and empirical processes. New York: Springer.
  • Windmeijer, F., H. Farbmacher, N. Davies, and G. D. Smith. 2019. On the use of the Lasso for instrumental variables estimation with some invalid instruments. Journal of the American Statistical Association 114 (527):1339–50. doi:10.1080/01621459.2018.1498346.
  • Xie, H., and J. Huang. 2009. SCAD-penalized regression in high-dimensional partially linear models. The Annals of Statistics 37 (2):673–96. doi:10.1214/07-AOS580.
  • Xue, L. G., and L. X. Zhu. 2007. Empirical likelihood semiparametric regression analysis for longitudinal data. Biometrika 94 (4):921–37. doi:10.1093/biomet/asm066.
  • Yang, Y. P., L. F. Chen, and P. X. 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.
  • Yuan, J. Y., P. X. Zhao, and W. G. 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.
  • 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.
  • Zhang, S., P. X. Zhao, G. R. Li, and W. L. Xu. 2019. Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data. Journal of Multivariate Analysis 171:37–52. doi:10.1016/j.jmva.2018.11.002.
  • Zhao, P. X., and G. R. 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. X., and L. G. 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.

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