High-Dimensional Spatial Quantile Function-on-Scalar Regression

TL;DR

This paper introduces a new spatial quantile function-on-scalar regression model that characterizes the entire conditional distribution of high-dimensional functional responses across spatial domains, combining quantile regression and copula techniques.

Contribution

It develops a novel modeling framework for high-dimensional spatial functional data, establishing theoretical convergence rates and providing an efficient algorithm for practical implementation.

Findings

The model accurately captures the conditional distribution of functional responses.

Theoretical minimax convergence rates are established for coefficient estimation.

Simulation and real data analyses demonstrate the method's effectiveness.

Abstract

This paper develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile regression and copula modeling, we are able to explicitly characterize the conditional distribution of the functional or image response on the whole spatial domain. Our method provides a comprehensive understanding of the effect of scalar covariates on functional responses across different quantile levels and also gives a practical way to generate new images for given covariate values. Theoretically, we establish the minimax rates of convergence for estimating coefficient functions under both fixed and random designs. We further develop an efficient primal-dual algorithm to handle high-dimensional image data. Simulations and real data analysis are conducted to examine the finite-sample performance.