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

Nengxiang Ling (), Rui Kan (), Philippe Vieu () and Shuyu Meng ()
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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

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 1, No 3, 39-70

Abstract: 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.

Keywords: Asymptotic properties; Semi-functional partially linear regression model; Missing at random; Functional data analysis (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00184-018-0688-6

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