, Volume 82, Issue 1, pp 39–70 | Cite as

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

  • Nengxiang Ling
  • Rui Kan
  • Philippe Vieu
  • Shuyu Meng


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 \({\mathscr {H}}\) with a semi-metric \(d\left( \cdot , \cdot \right) \). 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.


Asymptotic properties Semi-functional partially linear regression model Missing at random Functional data analysis 



The authors would like to appreciate the Editor in Chief and the two referees for their valuable comments and suggestions that are very helpful for them to improve the quality and presentation of the paper significantly. Ling’s work is supported by the National Social Science Funds of China (14ATJ005).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nengxiang Ling
    • 1
  • Rui Kan
    • 1
  • Philippe Vieu
    • 2
  • Shuyu Meng
    • 3
  1. 1.School of MathematicsHefei University of TechnologyHefeiChina
  2. 2.Institut de MathématiquesUniversité Paul SabatierToulouseFrance
  3. 3.School of ScienceNanjing University of Science and TechnologyNanjingChina

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