Single-index partially functional linear quantile regression

Abstract

Tecator dataset has been widely used in the content of functional data analysis. As far as we know, this dataset is only considered under mean regression, which is easily affected by outliers. However, there are 8 more fat samples and 17 more protein samples in this dataset, so, in this paper, we explore this dataset by quantile regression, which is a robust method. Single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function in the single-index component and the unknown slope function in the functional linear component. We establish the convergence rates and asymptotic normality of the estimators. Simulation studies and a real data application are presented to illustrate the performance of the proposed methodologies.