Estimation in Functional Linear Quantile Regression - FRIDAY, August 18th at 11am in ESB 4192

We consider the estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional of the covariate. There are two common approaches for modeling the conditional mean as a linear functional of the covariate. One is to use the functional principal components of the covariates as basis to represent the functional covariate effect. The other one is to extend the partial least square to model the functional effect. The former belongs to unsupervised method and has been generalized to functional linear quantile regression. The latter is a supervised method and is superior to the unsupervised PCA method. In this talk, we propose to use partial quantile regression and its tensor approximation to estimate the functional effect in functional linear quantile regression. Asymptotic properties have been studied and show the virtue of our method in large sample. Simulation study is conducted to compare it with existing methods. Real data examples are analyzed and some interesting findings are discovered.