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A Consistent Estimator for Model Structure and Variable Selection

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  • Wang, Taining
  • Zhang, Xiaoqi
  • Tian, Jinjing

Abstract

A kernel-based estimator is proposed for identifying the underlying structure of a nonparametric regression model from a wide range of alternatives known up to second-order derivatives. The estimator with modifications can further select relevant variables in the model. Under mild conditions, the estimator is shown to be consistent for both model structure and variable selection. The estimator is computationally efficient, can be easily deployed on a parallel computing system, and exhibits appealing finite sample performance through simulation studies. An empirical application is given to illustrate how the unknown underlying structure of a production function can be identified in practice.

Suggested Citation

  • Wang, Taining & Zhang, Xiaoqi & Tian, Jinjing, 2025. "A Consistent Estimator for Model Structure and Variable Selection," Econometrics and Statistics, Elsevier, vol. 34(C), pages 44-68.
    • Handle: RePEc:eee:ecosta:v:34:y:2025:i:c:p:44-68
    DOI: 10.1016/j.ecosta.2022.02.005
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    1. Behrendt, Simon & Schweikert, Karsten, 2021. "A Note on Adaptive Group Lasso for Structural Break Time Series," Econometrics and Statistics, Elsevier, vol. 17(C), pages 156-172.
    2. Lian, Heng & Meng, Jie & Zhao, Kaifeng, 2015. "Spline estimator for simultaneous variable selection and constant coefficient identification in high-dimensional generalized varying-coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 81-103.
    3. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, vol. 87(1), pages 145-165, August.
    6. Daniel J. Henderson & Chris Papageorgiou & Christopher F. Parmeter, 2012. "Growth Empirics without Parameters," Economic Journal, Royal Economic Society, vol. 122(559), pages 125-154, March.
    7. Judit Montoriol Garriga, 2006. "The Effect of Relationship Lending on Frim Performance," Working Papers 0605, Departament Empresa, Universitat Autònoma de Barcelona, revised Jun 2006.
    8. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    9. Zhang, Rui & Sun, Kai & Delgado, Michael S. & Kumbhakar, Subal C., 2012. "Productivity in China's high technology industry: Regional heterogeneity and R&D," Technological Forecasting and Social Change, Elsevier, vol. 79(1), pages 127-141.
    10. Yichao Wu & Leonard A. Stefanski, 2015. "Automatic structure recovery for additive models," Biometrika, Biometrika Trust, vol. 102(2), pages 381-395.
    11. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    12. Jingping Gu & Qi Li & Jui-Chung Yang, 2015. "Multivariate Local Polynomial Kernel Estimators: Leading Bias and Asymptotic Distribution," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 979-1010, December.
    13. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    14. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    15. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
    16. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    17. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    18. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    19. Yao, Feng & Wang, Taining & Tian, Jinjing & Kumbhakar, Subal C., 2018. "Estimation of a smooth coefficient zero-inefficiency panel stochastic frontier model: A semiparametric approach," Economics Letters, Elsevier, vol. 166(C), pages 25-30.
    20. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, vol. 91(2), pages 373-401, August.
    21. Risa Kato & Takayuki Shiohama, 2009. "Model and Variable Selection Procedures for Semiparametric Time Series Regression," Journal of Probability and Statistics, Hindawi, vol. 2009, pages 1-37, September.
    22. Zhang, Hao Helen & Cheng, Guang & Liu, Yufeng, 2011. "Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1099-1112.
    23. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    24. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    25. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    26. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    27. Maciak, Matúš, 2021. "Quantile LASSO in arbitrage-free option markets," Econometrics and Statistics, Elsevier, vol. 18(C), pages 106-116.
    28. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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