An abundance of high quality data sets requiring heavy tailed models necessitates reliablemethods of estimating the shape parameter governing the degree of tail heaviness.The Hill estimator is a popular method for doing this but its practical use isencumbered by several difficulties. We show...

In general, estimators of the extreme value index of i.i.d. random variables crucially depend on the sample fraction that is used for estimation. In case of the well-known Hill estimator the optimal number knopt of largest order statistics was given by Hall and Welsh (1985) as a function of some...

An abundance of high quality data sets requiring heavy tailed models necessitates reliablemethods of estimating the shape parameter governing the degree of tail heaviness.The Hill estimator is a popular method for doing this but its practical use isencumbered by several difficulties. We show...

An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several difficulties. We show...

Recently, a weighted approximation for the tail empirical distribution function has been developed (Approximations to the tail empirical distribution function with application to testing extreme value conditions. preprint, submitted for publication). We show that the same result can also be used...

Consider the problem of estimating the mean of a single normal random variable when the mean is known to be bounded. We establish the minimax affine estimator under zero-one loss and discuss minimal fixed-length affine confidence intervals. Moreover, the minimal length of arbitrary fixed-size...

We consider an extended version of a model proposed by Ledford and Tawn [Ledford, A.W., Tawn, J.A., 1997. Modelling dependence within joint tail regions. J. R. Stat. Soc. 59 (2), 475-499] for the joint tail distribution of a bivariate random vector, which essentially assumes an asymptotic power...