We extend extreme value statistics to independent data with possibly very different distributions. In particular, we present novel asymptotic normality results for the Hill estimator, which now estimates the extreme value index of the average distribution. Due to the heterogeneity, the...

Two time series of financial losses may be observed in different overlapping windows, serially dependent, heteroscedastic, and cross-sectionally dependent. Fitting a regression model to each of the two time series, we construct an improved least squares estimator in one series exploiting the...