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Partially linear varying coefficient models stratified by a functional covariate

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  • Maity, Arnab
  • Huang, Jianhua Z.

Abstract

We consider the problem of estimation in semiparametric varying coefficient models where the covariate modifying the varying coefficients is functional and is modeled nonparametrically. We develop a kernel-based estimator of the nonparametric component and a profiling estimator of the parametric component of the model, and derive their asymptotic properties. Specifically, we show the consistency of the nonparametric functional estimates and derive the asymptotic expansion of the estimates of the parametric component. We illustrate the performance of our methodology using a simulation study and a real data application.

Suggested Citation

  • Maity, Arnab & Huang, Jianhua Z., 2012. "Partially linear varying coefficient models stratified by a functional covariate," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1807-1814.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1807-1814
    DOI: 10.1016/j.spl.2012.06.002
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    References listed on IDEAS

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    1. F. Ferraty & P. Vieu, 2008. "Erratum of: ‘Non-parametric models for functional data, with application in regression, time-series prediction and curve discrimination’," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(2), pages 187-189.
    2. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    3. Heng Lian, 2011. "Functional partial linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 115-128.
    4. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
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    Cited by:

    1. Germán Aneiros & Nengxiang Ling & Philippe Vieu, 2015. "Error variance estimation in semi-functional partially linear regression models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(3), pages 316-330, September.
    2. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    3. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.

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