B0896
Title: Analysis of extremal behaviour using block sums and averages
Authors: Boris Beranger - University of New South Wales (Australia) [presenting]
Michael Stewart - University of Sydney (Australia)
Scott Sisson - University of New South Wales (Austria)
Abstract: In many environmental applications, it is common that a series of underlying raw observations are condensed into block sums (or averages) and that those summaries are the only source of information available for analysis. For example, raw observations of air pollutant levels are recorded at some weather stations every 5 minutes but only hourly averages are reported. It may be of interest to estimate the exceedance probability of a high threshold, or the quantile corresponding to a very small upper tail probability for the hourly averages. However, similar questions relating to the underlying raw observations might be of greater interest since they directly focus on the extremes of natural phenomena. We are interested in estimating the extremal behaviour of some underlying observations when only block sums and averages are available. We show that some progress can be made when the underlying distribution is heavy-tailed but relatively close to the Gumbel domain of attraction. We establish some theoretical properties of our estimators, and illustrate their performance through numerical experiments and on a pollution dataset.
