SMOOTH DENSITY SPATIAL QUANTILE REGRESSION.

Area of Science:

• Environmental statistics
• Statistical modeling
• Geostatistics

Background:

• Estimating covariate effects on the entire distribution is challenging.
• Existing methods may lack flexibility, especially for extreme values.
• Spatially-varying effects require advanced modeling techniques.

Purpose of the Study:

• To develop a flexible model-based method for estimating spatially-varying covariate effects on the quantile function.
• To allow for flexible modeling of distribution extremes and non-parametric flexibility in the center.
• To enable estimation of non-stationary covariance functions dependent on predictors.

Main Methods:

• Modeling the quantile function using I-spline basis functions and Pareto tail distributions.
• Ensuring differentiability of the density function.
• Estimating predictor-dependent, non-stationary covariance functions.

Main Results:

• The proposed method yields more efficient estimates of predictor effects compared to existing methods.
• The model demonstrates superior performance, particularly for heavy-tailed distributions.
• The simulation study confirms the method's effectiveness.

Conclusions:

• The developed model offers a desirable and flexible approach for analyzing spatially-varying covariate effects.
• It provides robust estimation, especially in the presence of heavy tails.
• The method is applicable to real-world environmental monitoring, such as assessing emission impacts.