Tensor Approximation in Functional Linear Quantile Regression

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: International Chinese Statistical Association
• Author(s): Linglong Kong* and Dengdeng Yu and Ivan Mizera
• Companies: University of Alberta and University of Alberta and University of Alberta
• Keywords: Tensor ; functional data analysis ; Quantile regression ; Partial least square ; Neuroimaging data analysis ; Supervised learning

Abstract

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 later 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. A real data example in stroke study is analyzed and some interesting findings are discovered.