A1232
Title: Covariate-adjusted conditional quantile regression for functional data
Authors: Salil Koner - University of California, Riverside (United States) [presenting]
Abstract: Quantile regression is a powerful tool in functional data analysis, as it enables the characterization of heterogeneity, robustness to outliers and departures from normality, and the investigation of tail behavior. While pointwise conditional quantile functions are straightforward to model, they do not fully capture the distributional structure of functional responses. Spatial quantiles provide a principled framework for describing the depth and centrality of a function within a functional data cloud. A spline-based methodology is developed for estimating conditional spatial quantiles when both the response and covariates are functional. The proposed framework accommodates data observed on either dense or sparse domains. Estimation is carried out by solving a not-strictly convex optimization problem using a fast and efficient minorization-maximization (MM) algorithm, which yields a globally unique minimizer. Extensive simulation studies demonstrate the strong finite-sample performance of the approach, including under sparse sampling designs. The method's practical utility is further illustrated by applying it to real-world functional data.
