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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.03754 |
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Table of Contents:
- We address the problem of prediction for extreme observations by proposing an extremal linear prediction method. We construct an inner product space of nonnegative random variables derived from transformed-linear combinations of independent regularly varying random variables. Under a reasonable modeling assumption, the matrix of inner products corresponds to the tail pairwise dependence matrix, which can be easily estimated. We derive the optimal transformed-linear predictor via the projection theorem, which yields a predictor with the same form as the best linear unbiased predictor in non-extreme settings. We quantify uncertainty for prediction errors by constructing prediction intervals based on the geometry of regular variation. We demonstrate the effectiveness of our method through a simulation study and its applications to predicting high pollution levels, and extreme precipitation.