A1230
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: Spatially varying coefficient models provide a flexible extension of linear regression models to capture the non-stationarity of regression coefficients across space. However, its research mostly focuses on mean regression settings. Quantile regression gives a more comprehensive analysis of the effect of the predictors on the response when one is interested in the full distributional properties of the response or when assumptions on the mean regression are violated. A flexible quantile spatially varying coefficient model is introduced to assess how conditional quantiles of the response depend on covariates, allowing the coefficient function to vary with spatial location. The model can be used to explore spatial non-stationarity of regression relationships for heterogeneous spatial data distributed over a domain of a complex or irregular shape. To estimate the coefficient functions of the model over a complex spatial domain, a quantile regression method is proposed that adopts the bivariate penalized spline technique to approximate the unknown functional coefficients. The L2 convergence of the proposed estimator with an optimal convergence rate under some regularity conditions is established. Also, an efficient algorithm based on the alternating direction method of multipliers is developed to solve the optimization problem. Numerical studies examine the finite sample performance of the proposed method.
