Estimation and Inference of Quantile Spatially Varying Coefficient Models Over Complicated Domains.

Area of Science:

• Spatial Statistics
• Geostatistics
• Econometrics

Background:

• Traditional regression models often assume stationarity, which is frequently violated in spatial data.
• Analyzing spatial data requires methods that can capture both quantile-specific relationships and spatial heterogeneity.
• Existing methods may struggle with complex or irregular spatial domains.

Purpose of the Study:

• To present a flexible quantile spatially varying coefficient model (QSVCM) for spatial regression analysis.
• To enable the assessment of conditional quantile dependence on covariates while accounting for spatial nonstationarity.
• To facilitate the interpretation of heterogeneity in spatial data across complex domains.

Main Methods:

• Utilizes bivariate penalized splines in triangulation for estimating unknown functional coefficients.
• Employs an efficient optimization algorithm based on the alternating direction method of multipliers (ADMM).
• Develops wild residual bootstrap-based pointwise confidence intervals and conformal prediction intervals.

Main Results:

• Establishes $L_2$ convergence of the proposed estimators with optimal convergence rates.
• Demonstrates the effectiveness and performance of the QSVCM through simulation studies.
• Provides reliable prediction intervals for the response variable.

Conclusions:

• The proposed QSVCM offers a flexible and powerful approach for analyzing spatial data with nonstationarity.
• The method effectively captures quantile-specific relationships and spatial heterogeneity.
• Demonstrates practical applicability through analysis of real-world mortality and particulate matter datasets.