Abstract

This article 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.

摘要

本文开发了一种新的空间分位数函数标量回归模型，该模型研究了给定标量预测变量的高维函数响应的条件空间分布。凭借分位数回归和 copula 建模的优势，我们能够明确地描述整个空间域上功能或图像响应的条件分布。我们的方法提供了对标量协变量对不同分位数水平的功能响应的影响的全面理解，并提供了一种实用的方法来为给定的协变量值生成新图像。从理论上讲，我们建立了在固定和随机设计下估计系数函数的极小极大收敛率。我们进一步开发了一种有效的原始对偶算法来处理高维图像数据。