Stat Sin. 2021;31. doi: 10.5705/ss.202019.0002.

SMOOTH DENSITY SPATIAL QUANTILE REGRESSION.

Statistica Sinica

Halley Brantley, Montserrat Fuentes, Joseph Guinness, Eben Thoma

PMID: 34987278 PMCID: PMC8725653 DOI: 10.5705/ss.202019.0002

Abstract

We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially-varying effects of covariates on the quantile function. By modeling the quantile function as a combination of I-spline basis functions and Pareto tail distributions, we allow for flexible parametric modeling of the extremes while preserving non-parametric flexibility in the center of the distribution. We further establish that the model guarantees the desired degree of differentiability in the density function and enables the estimation of non-stationary covariance functions dependent on the predictors. We demonstrate through a simulation study that the proposed method produces more efficient estimates of the effects of predictors than other methods, particularly in distributions with heavy tails. To illustrate the utility of the model we apply it to measurements of benzene collected around an oil refinery to determine the effect of an emission source within the refinery on the distribution of the fence line measurements.

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Publication Types

• Journal Article

Grant support

• EPA999999/ImEPA/Intramural EPA/United States
• R01 ES027892/ES/NIEHS NIH HHS/United States