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

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 ℋ with a semi-metric 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.