Conditional extremes

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This paper develops a theory of high and low (extremal) quantile regression: the linear models, estimation, and inference. In particular, the models coherently combine the convenient, flexible linearity with the extreme-value-theoretic restrictions on tails and the general heteroscedasticity forms. Within these models, the limit laws for extremal quantile regression statistics are obtained unde...

Conference on Conditional Independence Structures and Extremes

s of Talks Sven Buhl, Technical University of Munich, Germany Semiparametric estimation for max-stable space-time processes Abstract: We propose a semiparametric estimation procedure based on a closed form expression of the extremogram (cf. [2], [3], [4]) to estimate the model parameters in a max-stable space-time process. We establish the asymptotic properties of the resulting parameter estima...

A Note on the Asymptotic Behavior of Conditional Extremes

Suppose (X1,Zl)"'" (Xn,Zn) are LLd. as (X,Z). Let Mn,k be the maximum of all Z. 's for which X. is among the k-nearest neighbors of X=xO' It is shown that M k has the lI , same asymptotic distribution as the maximum of k LLd. copies of the random variable Z given X=xO' Hence, the asymptotic results for Li.d. observations are applicable to this· situation as well. Key' words: nearest neighbor, c...

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

− This paper is dedicated to the estimation of extreme quantiles and the 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 and their finite sample properties are illustrated on a simulation...

Meteorological Extremes