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Semiparametric method for model structure discovery in additive regression models

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  • Yoshida, Takuma

Abstract

In regression analysis, there are two typical approaches, parametric methods and nonparametric methods. If the prior information of the structure of the regression function is obtained, a parametric method is preferred since they are efficient and easily interpreted. When the model is misspecified, on the other hand, parametric estimators do not work well. Therefore, it is important to check whether the parametric model assumption is valid. To simultaneously discover the model structure and estimate the regression function in additive regression models, a new semiparametric method is proposed. First, a parametric model is prepared and its estimator is obtained for all additive components. Next, for the residual data associated with the parametric estimator, a nonparametric method is applied. The final estimator is constructed by summing the parametric estimator and the nonparametric estimator of the residual data. In the second-step estimation, the B-spline method with an adaptive group lasso penalty is utilized. For each additive component, if the nonparametric estimator becomes the zero function, the final estimator is reduced to a parametric estimator. In other words, the model structure can then be discovered. The asymptotic properties of the proposed estimator are shown. A numerical study via a Monte Carlo simulation and a real data application are presented.

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  • Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    • Handle: RePEc:eee:ecosta:v:5:y:2018:i:c:p:124-136
    DOI: 10.1016/j.ecosta.2017.02.005
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    1. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    2. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    3. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    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. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. El Ghouch, Anouar & Genton, Marc G., 2009. "Local Polynomial Quantile Regression With Parametric Features," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1416-1429.
    7. Yichao Wu & Leonard A. Stefanski, 2015. "Automatic structure recovery for additive models," Biometrika, Biometrika Trust, vol. 102(2), pages 381-395.
    8. Opsomer, Jean D. & Ruppert, D., 1998. "A Fully Automated Bandwidth Selection Method for Fitting Additive Models," Staff General Research Papers Archive 1176, Iowa State University, Department of Economics.
    9. 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.
    10. Jianqing Fan & Arnab Maity & Yihui Wang & Yichao Wu, 2013. "Parametrically guided generalised additive models with application to mergers and acquisitions data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 109-128, March.
    11. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    12. Carlos Martins-Filho & Santosh Mishra & Aman Ullah, 2008. "A Class of Improved Parametrically Guided Nonparametric Regression Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 542-573.
    13. 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.
    14. Liu, Rong & Yang, Lijian, 2010. "Spline-Backfitted Kernel Smoothing Of Additive Coefficient Model," Econometric Theory, Cambridge University Press, vol. 26(1), pages 29-59, February.
    15. 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.
    16. 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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