A note on the asymptotic behavior of conditional extremes

Gangopadhyay, Ashis

doi:10.1016/0167-7152(94)00218-w

Cited by 8 publications

(9 citation statements)

References 3 publications

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“…when covariate information is available, only few results exist. We refer to [18], Theorem 3.5.2, for the approximation of the nearest neighbors distribution using the Hellinger distance and to [20] for the study of their asymptotic distribution. Our second main result establishes the asymptotic normality of our estimators.…”

Section: Resultsmentioning

confidence: 99%

A moving window approach for nonparametric estimation of the conditional tail index

Gardès

Girard

2008

Journal of Multivariate Analysis

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Rapport de rechercheInternational audienceWe present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study

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Section: Resultsmentioning

confidence: 99%

A moving window approach for nonparametric estimation of the conditional tail index

Gardès

Girard

2008

Journal of Multivariate Analysis

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“…It establishes a representation of the log-spacings in terms of standard exponential random variables which is the cornerstone of the proof of Theorem 1. We refer to [15], Theorem 3.5.2, for the approximation of the nearest neighbors distribution using the Hellinger distance and to [16] for the study of their asymptotic distribution. …”

Section: Proofs Of Main Resultsmentioning

confidence: 99%

Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels

Gardès

Girard²

2010

Extremes

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− This paper is dedicated to the estimation of extreme quantiles and tail index from heavy-tailed distributions when a covariate is recorded simultaneously with the quantity of interest. A nearest neighbor approach is used to construct our estimators. Their asymptotic normality is established under mild regularity conditions. An application to the estimation of return periods of extreme rainfalls in the Cévennes-Vivarais region is provided.

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“…Fully non-parametric estimators have been rst introduced in [6,10] through respectively local polynomial and spline models. We also refer to [12, Theorem 3.5.2] for the approximation of the nearest neighbors distribution using the Hellinger distance and to [13] for the study of their asymptotic distribution. Focusing on the estimation of the tail-index of the conditional distribution of Y given x, moving windows and nearest neighbors approaches are developed respectively by [15,16] in a xed design setting.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

Ahmad

Dème

Diop

et al. 2019

Dependence Modeling

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We introduce a location-scale model for conditional heavy-tailed distributions when the covariate is deterministic. First, nonparametric estimators of the location and scale functions are introduced. Second, an estimator of the conditional extreme-value index is derived. The asymptotic properties of the estimators are established under mild assumptions and their finite sample properties are illustrated both on simulated and real data.

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A note on the asymptotic behavior of conditional extremes

Cited by 8 publications

References 3 publications

A moving window approach for nonparametric estimation of the conditional tail index

A moving window approach for nonparametric estimation of the conditional tail index

Conditional extremes from heavy-tailed distributions: an application to the estimation of extreme rainfall return levels

Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions

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