Transformed-Linear Prediction for Extremes

• Activity Number: 131 - Methods for Spatial, Temporal, and Spatio-Temporal Data
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Jeongjin Lee* and Daniel Cooley
• Companies: Colorado State University and Colorado State University
• Keywords: The best transformed-linear prediction; Tail pairwise dependence matrix; Completely positive decomposition

Abstract

We derive the best transformed-linear predictor for extremes on the positive orthant within the vector space which is a set of transformed-linear combinations of regularly varying random variables with finite coefficients. The optimized weights for the transformed-linear predictor are represented by the tail pairwise dependence matrix (TPDM) as analogous to those for the BLUP are expressed by a covariance matrix in Gaussian cases. We construct uncertainty quantification using the polar geometry of regular variation utilizing a completely positive decomposition of the TPDM. We produce a 95% joint probability region and 95% conditional prediction intervals given large values of the transformed-linear predictor. We apply our method to the NO2 pollution data in Washington, DC and to daily returns of 30 industry portfolios and obtain good coverage rates.