A0427
Title: Estimation and inference of quantile spatially varying coefficient models over complicated domains
Authors: Myungjin Kim - Kyungpook National University (Korea, South) [presenting]
Lily Wang - George Mason University (United States)
Huixia Judy Wang - George Washington University (United States)
Abstract: The aim is to present 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. The approach facilitates learning and interpreting heterogeneity in spatial data distributed over complex or irregular domains. A quantile regression method that uses bivariate penalized splines in triangulation is introduced to estimate unknown functional coefficients. The L2 convergence of the proposed estimators is established, demonstrating their optimal convergence rate under certain regularity conditions. An efficient optimization algorithm is developed using the alternating direction method of multipliers (ADMM). Wild residual bootstrap-based pointwise confidence intervals are developed for the QSVCM quantile coefficients. Furthermore, reliable conformal prediction intervals are constructed for the response variable using the proposed QSVCM. Simulation studies show the remarkable performance of the proposed methods. Lastly, the practical applicability of the methods is illustrated by analyzing the mortality dataset and the supplementary particulate matter (PM) dataset in the United States.
