Spatial Quantile Regression for Data With Smooth Density Functions
Brantley, H., M. Fuentes, J. Guinness, AND E. Thoma. Spatial Quantile Regression for Data With Smooth Density Functions. Statistica Sinica. International Chinese Statistical Association (ICSA), Statesboro, GA, 31(3):1167-1187, (2021). https://doi.org/10.5705/ss.202019.0002
Energy production operations, refineries, chemical plants, and other industries and waste facilities can emit air pollutants and odorous compounds from fugitive leaks, process malfunctions, and area sources that are hard to detect and manage. From the shared perspective of industries, regulators, and communities, improved understanding of stochastic industrial sources (SIS) can yield many benefits such as safer working environments, cost savings through reduced product loss, lower airshed impacts, and improved community relations. The emergence of lower-cost sensors, time integrated samples, and inverse modeling approaches, is enabling new cost-effective ways to detect and analyze SIS emissions. Under its next generation emissions measurement (NGEM) program, EPA is working with a range of partners to develop and test NGEM tools that can assist facilities in detection and management of sources. As described below, the following product contributes to the general advancement and communication of NGEM concepts.
We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially varying effects of covariates on a 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 the nonparametric 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 us to estimate nonstationary covariance functions that are dependent on the predictors. We use a simulation study to show that the proposed method outperforms other methods in terms of producing efficient estimates of the effects of predictors, 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.