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Semi-functional partially linear regression model with responses missing at random

Author

Listed:
  • Nengxiang Ling

    (Hefei University of Technology)

  • Rui Kan

    (Hefei University of Technology)

  • Philippe Vieu

    (Université Paul Sabatier)

  • Shuyu Meng

    (Nanjing University of Science and Technology)

Abstract

This paper focuses on semi-functional partially linear regression model, where a scalar response variable with missing at random is explained by a sum of an unknown linear combination of the components of multivariate random variables and an unknown transformation of a functional random variable which takes its value in a semi-metric abstract space $${\mathscr {H}}$$ H with a semi-metric $$d\left( \cdot , \cdot \right) $$ d · , · . The main purpose of this paper is to construct the estimators of unknown parameters and an unknown regression operator respectively. Then some asymptotic properties of the estimators such as almost sure convergence rates of the nonparametric component and asymptotic distribution of the parametric one are obtained under some mild conditions. Furthermore, a simulation study is carried out to evaluate the finite sample performances of the estimators. Finally, an application to real data analysis for food fat predictions shows the usefulness of the proposed methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:1:d:10.1007_s00184-018-0688-6
    DOI: 10.1007/s00184-018-0688-6
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    References listed on IDEAS

    as
    1. 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.
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    10. Efromovich, Sam, 2011. "Nonparametric Regression With Predictors Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 306-319.
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    Cited by:

    1. Nengxiang Ling & Lilei Cheng & Philippe Vieu & Hui Ding, 2022. "Missing responses at random in functional single index model for time series data," Statistical Papers, Springer, vol. 63(2), pages 665-692, April.
    2. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).

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