It has been known for a long time that for bootstrapping the probability distribution of the maximum of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. See Jun Shao and Dongsheng Tu (1995), Ex. 3.9,p. 123. We show that the same is true...

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on...

Asymptotic tail probabilities for bivariate linear combinations of subexponential random variables are given. These results are applied to explain the joint movements of the stocks of reinsurers. Portfolio investment and retrocession practices in the reinsurance industry, for reasons of...

We present a framework for statistical analysis of discrete event systems which combines tools such as simulation of marked point processes, likelihood methods, kernel density estimation and stochastic approximation to enable statistical analysis of the discrete event system, even if...