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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
Abstract #317842
Title: Transformed-Linear Prediction for Extremes
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

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.

Authors who are presenting talks have a * after their name.

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