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Estimation and variable selection for partial functional linear regression

Author

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  • Qingguo Tang

    (Nanjing University of Science and Technology)

  • Peng Jin

    (Nanjing University of Science and Technology)

Abstract

We propose a new estimation procedure for estimating the unknown parameters and function in partial functional linear regression. The asymptotic distribution of the estimator of the vector of slope parameters is derived, and the global convergence rate of the estimator of unknown slope function is established under suitable norm. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Based on the proposed estimation procedure, we further construct the penalized regression estimators and establish their variable selection consistency and oracle properties. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about the real estate data is used to illustrate our proposed methodology.

Suggested Citation

  • Qingguo Tang & Peng Jin, 2019. "Estimation and variable selection for partial functional linear regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 475-501, December.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:4:d:10.1007_s10182-018-00342-0
    DOI: 10.1007/s10182-018-00342-0
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    References listed on IDEAS

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    1. 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.
    2. Liang, Hua & Li, Runze, 2009. "Variable Selection for Partially Linear Models With Measurement Errors," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 234-248.
    3. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    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. Shin, Hyejin & Lee, Myung Hee, 2012. "On prediction rate in partial functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 93-106, January.
    6. Hankin, Robin K. S., 2015. "Circular Statistics in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(b05).
    7. Daowen Zhang & Xihong Lin & MaryFran Sowers, 2007. "Two-Stage Functional Mixed Models for Evaluating the Effect of Longitudinal Covariate Profiles on a Scalar Outcome," Biometrics, The International Biometric Society, vol. 63(2), pages 351-362, June.
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