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Title: Quantile regression under spatial noise correlation Authors:  Surya Tokdar - Duke University (United States) [presenting]
Abstract: Quantile regression is widely adopted for regression analyses in ecology, economics, education, public health and climatology. In QR, one replaces the standard regression equation of the mean with a similar equation for a quantile at a given quantile level of interest. But the real strength of QR lies in the possibility of analyzing any quantile level of interest, and perhaps more importantly, contrasting many such analyses against each other with fascinating consequences. Despite the popularity of QR, it is only recently that an analysis framework has been developed which transforms the four-decade-old idea into a model-based inference and prediction technique in its full generality. In doing so, the new joint estimation framework has opened doors to many important advancements of the QR analysis technique to address additional data complications. The focus is on extending quantile regression to analyzing geolocated data while adjusting for spatial noise correlation. We will show how the considered modeling framework allows a new interpretation of 'noise' in the QR context, and how one may seamlessly generalize this estimation framework to account for a wide variety of noise dependency, including tail dependence appropriate for heavy-tailed data. The new method is applied to air quality and wildfire risk analyses.