Consider a tandem queue consisting of two single-server queues in series, with a Poisson arrival process at the first queue and arbitrarily distributed service times, which for any customer are identical in both queues. For this tandem queue, we relate the tail behaviour of the sojourn time...

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...

In this paper we analyze the asymptotic properties of the popularly used distribution tail estimator by B. Hill (1975), for heavy-tailed heterogenous, dependent processes. We prove the Hill estimator is weakly consistent for functionals of mixingales and L1-approximable processes with regularly...

We develop a non-parametric test of tail-specific extremal serial dependence for possibly heavy-tailed time series. The test statistic is asymptotically chi-squared under a null of "extremal white noise", as long as extremes of the time series are Near-Epoch-Dependent on the extremes of some...

This paper considers tail shape inference techniques robust to substantial degrees of serial dependence and heterogeneity. We detail a new kernel estimator of the asymptotic variance and the exact small sample mean-squared-error, and a simple representation of the bias of the B. Hill (1975) tail...

We establish functional central limit theorems for a broad class of dependent, heterogeneous tail arrays encountered in the extreme value literature, including extremal exceedances, tail empirical processes and tail empirical quantile processes. We trim dependence assumptions down to a minimum...

Let X and Y be two nonnegative dependent random variables according to a copula function. Under appropriate conditions, the closure property of the product XY is derived when X belongs to class S and R, respectively. Some examples are provided to illustrate the impact of the dependence structure...

The quantification of diversification benefits due to risk aggregation has received more attention in the recent literature. In this paper, we establish second-order expansions of the risk concentration based on the risk measure of conditional tail expectation for a portfolio of n independent...