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Sparse estimation for functional semiparametric additive models

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  • Sang, Peijun
  • Lockhart, Richard A.
  • Cao, Jiguo

Abstract

We propose a functional semiparametric additive model for the effects of a functional covariate and several scalar covariates and a scalar response. The effect of the functional covariate is modeled nonparametrically, while a linear form is adopted to model the effects of the scalar covariates. This strategy can enhance flexibility in modeling the effect of the functional covariate and maintain interpretability for the effects of scalar covariates simultaneously. We develop the method for estimating the functional semiparametric additive model by smoothing and selecting non-vanishing components for the functional covariate. Asymptotic properties of our method are also established. Two simulation studies are implemented to compare our method with various conventional methods. We demonstrate our method with two real applications.

Suggested Citation

  • Sang, Peijun & Lockhart, Richard A. & Cao, Jiguo, 2018. "Sparse estimation for functional semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 105-118.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:105-118
    DOI: 10.1016/j.jmva.2018.06.010
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    Cited by:

    1. Bin Yang & Min Chen & Tong Su & Jianjun Zhou, 2023. "Robust Estimation for Semi-Functional Linear Model with Autoregressive Errors," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Tang, Qingguo & Tu, Wei & Kong, Linglong, 2023. "Estimation for partial functional partially linear additive model," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    3. Xiong Cai & Liugen Xue & Xiaolong Pu & Xingyu Yan, 2021. "Efficient Estimation for Varying-Coefficient Mixed Effects Models with Functional Response Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 467-495, May.

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