High-Dimensional Spatial Quantile Function-on-Scalar Regression
本文提出一种新的空间分位数函数对标量回归模型，结合分位数回归和Copula建模，刻画高维函数型响应在标量预测变量下的条件空间分布，并给出估计系数函数的极小化极大收敛率及高效算法。
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.