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 Name: Jochem Oorschot

Talk Title: Extreme U-statistics

Abstract: (joint work with Johan Segers & Chen Zhou) One-sample U-statistics generalize the notion of averages and lead to minimum-variance unbiased estimators. Segers (2001) considered U-statistics for sequences of location-scale invariant kernels whose degree grows with the sample size and which depend only on the largest of their arguments. By ensuring that the kernel’s expectation converges to a function of the extreme value index, it is possible to construct consistent estimators of the latter using such Extreme U-statistics. The all-block maxima in Oorschot & Zhou follow a similar logic, by recording the maxima of all sub-samples of observations of a given size. In this paper we explore the asymptotic normality of  general Extreme-U-statistics. The theory draws largely from the one of U-statistics by considering kernels applied to blocks of intermediate length m(n) that grow as a function of the sample size n.

Oorschot, J. and Zhou, C. (2020). All Block Maxima method for estimating the extreme value index. arXiv.

Segers, J. (2001). Extremes of a random sample: Limit theorems and statistical applications. PhD thesis, KU Leuven.

This talk is [a contributed talk / an invited talk / a plenary lecture] at EVA 2021.