High-Dimensional Spatial Quantile Function-on-Scalar Regression

• 成果类型: Article
• 署名作者: Zhang, Zhengwu; Wang, Xiao; Kong, Linglong; Zhu, Hongtu
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Purdue University System; Purdue University; University of Alberta; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1870984
• 发表日期: 2022
• 页码: 1563-1578
• 关键词: laplacian tortoise

摘要

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.