Estimation and testing for time-varying quantile single-index models with longitudinal data

Regarding semiparametric quantile regression, the existing literature is largely focused on independent observations. A time-varying quantile single-index model suitable for complex data is proposed, in which the responses and covariates are longitudinal/functional, with measurements taken at discrete time points. A statistic for testing whether the time effect is significant is developed. The proposed methodology is illustrated using Monte Carlo simulation and empirical data analysis.