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Estimation for partial functional partially linear additive model

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  • Tang, Qingguo
  • Tu, Wei
  • Kong, Linglong

Abstract

A class of scalar-on-function regression estimating the nonparametric effects of a functional predictor and semiparametric effects of multivariate scalar predictors is investigated. The proposed model is motivated by applications considering both functional and scalar predictors with possibly nonlinear effects. A two-step estimation procedure together with functional principal components analysis allows the simultaneous estimation of nonlinear effects of both the functional and scalar predictors. The computation of the proposed estimators is efficient and does not require iterative algorithms, which is desirable for high dimensional setting. Asymptotic properties such as convergence rate and asymptotic normality have been established. Finite sample performances are studied through simulations and data analysis in functional neuroimaging and real estate analytic.

Suggested Citation

  • Tang, Qingguo & Tu, Wei & Kong, Linglong, 2023. "Estimation for partial functional partially linear additive model," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:csdana:v:177:y:2023:i:c:s0167947322001645
    DOI: 10.1016/j.csda.2022.107584
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    References listed on IDEAS

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    1. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    4. Kehui Chen & Hans‐Georg Müller, 2012. "Conditional quantile analysis when covariates are functions, with application to growth data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 67-89, January.
    5. Zhu, Hongtu & Zhang, Heping & Ibrahim, Joseph G. & Peterson, Bradley S., 2007. "Statistical Analysis of Diffusion Tensors in Diffusion-Weighted Magnetic Resonance Imaging Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1085-1102, December.
    6. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    7. Raymond K. W. Wong & Yehua Li & Zhengyuan Zhu, 2019. "Partially Linear Functional Additive Models for Multivariate Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 406-418, January.
    8. G. Aneiros & P. Vieu, 2016. "Sparse nonparametric model for regression with functional covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 839-859, October.
    9. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    10. 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.
    11. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
    12. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.
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