Spatial dependence and space-time trend in extreme events: Space-time trend in extremes

John H.J. Einmahl; Ana Ferreira; Laurens de Haan; Claudia Neves; Chen Zhou

doi:10.1214/21-AOS2067

Spatial dependence and space-time trend in extreme events: Space-time trend in extremes

John H.J. Einmahl, Ana Ferreira, Laurens de Haan, Claudia Neves, Chen Zhou^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

175 Downloads (Pure)

Abstract

he statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.

Original language	English
Article number	1
Pages (from-to)	30-52
Journal	ANNALS OF STATISTICS
Volume	50
Issue number	1
DOIs	https://doi.org/10.1214/21-AOS2067
Publication status	Published - 1 Feb 2022

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AOS2002-007R2A0

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title = "Spatial dependence and space-time trend in extreme events: Space-time trend in extremes",

abstract = "he statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.",

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T1 - Spatial dependence and space-time trend in extreme events

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AU - Einmahl, John H.J.

AU - Ferreira, Ana

AU - de Haan, Laurens

AU - Neves, Claudia

AU - Zhou, Chen

PY - 2022/2/1

Y1 - 2022/2/1

N2 - he statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.

AB - he statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the common extreme value index can be estimated via a pseudo-maximum likelihood procedure based on pooling all (non-stationary and dependent) observations. Our leading example and application is rainfall in Northern Germany.

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DO - 10.1214/21-AOS2067

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JO - ANNALS OF STATISTICS

JF - ANNALS OF STATISTICS

IS - 1

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Spatial dependence and space-time trend in extreme events: Space-time trend in extremes

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