Estimation and Inference of Quantile Spatially Varying Coefficient Models Over Complicated Domains
提出一种灵活的分位数空间变系数模型，用于分析复杂或不规则区域上的空间数据，通过三角剖分中的双变量惩罚样条估计系数，并开发了基于ADMM的优化算法和自助法置信区间，适用于死亡率等数据集。
This article presents a flexible quantile spatially varying coefficient model (QSVCM) for the regression analysis of spatial data. The proposed model enables researchers to assess the dependence of conditional quantiles of the response variable on covariates while accounting for spatial nonstationarity. Our approach facilitates learning and interpreting heterogeneity in spatial data distributed over complex or irregular domains. We introduce a quantile regression method that uses bivariate penalized splines in triangulation to estimate unknown functional coefficients. We establish the L2 convergence of the proposed estimators, demonstrating their optimal convergence rate under certain regularity conditions. An efficient optimization algorithm is developed using the alternating direction method of multipliers (ADMM). We develop wild residual bootstrap-based pointwise confidence intervals for the QSVCM quantile coefficients. Furthermore, we construct reliable conformal prediction intervals for the response variable using the proposed QSVCM. Simulation studies show the remarkable performance of the proposed methods. Lastly, we illustrate the practical applicability of our methods by analyzing the mortality dataset and the supplementary particulate matter (PM) dataset in the United States. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.