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Name: Jeongjin Lee 

Talk Title: Transformed-linear combination of regularly varying random variables and linear prediction for extremes.

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.

This talk is a contributed talk at EVA 2021. View the programme here.