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Semi-functional partial linear regression with measurement error: an approach based on kNN estimation

Author

Listed:
  • Silvia Novo

    (Universidad Carlos III de Madrid
    Instituto Flores de Lemus
    UC3M-Santander Big Data Institute)

  • Germán Aneiros

    (Universidade da Coruña
    Centro de Investigación en Tecnologías de la Información y las Comunicaciones (CITIC))

  • Philippe Vieu

    (Université Paul Sabatier)

Abstract

This paper focuses on a semi-parametric regression model in which the response variable is explained by the sum of two components. One of them is parametric (linear), the corresponding explanatory variable is measured with additive error and its dimension is finite (p). The other component models, in a nonparametric way, the effect of a functional variable (infinite dimension) on the response. kNN-based estimators are proposed for each component, and some asymptotic results are obtained. A simulation study illustrates the behaviour of such estimators for finite sample sizes, while an application to real data shows the usefulness of our proposal.

Suggested Citation

  • Silvia Novo & Germán Aneiros & Philippe Vieu, 2025. "Semi-functional partial linear regression with measurement error: an approach based on kNN estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 235-261, March.
    • Handle: RePEc:spr:testjl:v:34:y:2025:i:1:d:10.1007_s11749-024-00957-3
    DOI: 10.1007/s11749-024-00957-3
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    References listed on IDEAS

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    1. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Silvia Novo & Germán Aneiros & Philippe Vieu, 2019. "Automatic and location-adaptive estimation in functional single-index regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(2), pages 364-392, April.
    3. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
    4. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    5. Nengxiang Ling & Germán Aneiros & Philippe Vieu, 2020. "kNN estimation in functional partial linear modeling," Statistical Papers, Springer, vol. 61(1), pages 423-444, February.
    6. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.
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    8. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    9. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    10. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    11. 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.
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    13. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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