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...

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...