# Extremal Behavior of Aggregated Data with an Application to Downscaling

arXiv: https://arxiv.org/abs/1712.09816 · HTML: https://mlsanity.com/paper/1712.09816/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2017.

## Built on by (most cited first, 1 of 1)

- [Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks](https://mlsanity.com/paper/2111.00267/) (2021)

## Abstract (arXiv)

The distribution of spatially aggregated data from a stochastic process X may exhibit a different tail behavior than its marginal distributions. For a large class of aggregating functionals ℓ we introduce the ℓ-extremal coefficient that quantifies this difference as a function of the extremal spatial dependence in X. We also obtain the joint extremal dependence for multiple aggregation functionals applied to the same process. Explicit formulas for the ℓ-extremal coefficients and multivariate dependence structures are derived in important special cases. The results provide a theoretical link between the extremal distribution of the aggregated data and the corresponding underlying process, which we exploit to develop a method for statistical downscaling. We apply our framework to downscale daily temperature maxima in the south of France from a gridded data set and use our model to generate high resolution maps of the warmest day during the 2003 heatwave.