Semiparametric function-on-function quantile regression model with dynamic single-index interactions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

View graph of relations


Related Research Unit(s)


Original languageEnglish
Article number107727
Journal / PublicationComputational Statistics and Data Analysis
Online published13 Feb 2023
Publication statusPublished - Jun 2023


In this paper we propose a new semiparametric function-on-function quantile regression model with time-dynamic single-index interactions. Our model is very flexible in taking into account of the nonlinear time-dynamic interaction effects of the multivariate longitudinal/functional covariates on the longitudinal response, that most existing quantile regression models for longitudinal data are special cases of our proposed model. We propose to approximate the bivariate nonparametric coefficient functions by tensor product B-splines, and employ a check loss minimization approach to estimate the bivariate coefficient functions and the index parameter vector. Under some mild conditions, we establish the asymptotic normality of the estimated single-index coefficients using projection orthogonalization technique, and obtain the convergence rates of the estimated bivariate coefficient functions. Furthermore, we propose a score test to examine whether there exist interaction effects between the covariates. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis. © 2023 Elsevier B.V.

Research Area(s)

  • B-spline, Check loss minimization, Functional data, Score test, Semiparametric quantile regression, Single-index interaction