Remarks on data selection

The rules for selecting {XOut(j)}jj=1 from {X(i)}™=1 are not uniquely determined. This allows the analyst to explore various climate system properties regarding extremes.

One area is threshold selection in the POT approach. Besides allowing time-dependence, the size can be adjusted. A high (low) threshold size for maxima detection leads evidently to fewer (more) cases and, hence, to more conservative (liberal) results but likely also to wider (narrower) CIs. Furthermore, a too low threshold may lead to violations of the conditions of convergence to an extreme value distribution. Data in form of event times have implicitly also undergone a threshold selection. The documentary data about Elbe floods, for example, were critically screened (Mudelsee et al. 2003) whether there is enough evidence that merits inclusion into the flood record or there had instead been just an elevated water level noticed by a hypercritical observer.

For block extremes, the adjustable parameter is the block length. In the case of original data X(i) with even spacing, this corresponds to a fixed number, k, of X(i) values per block. In the case of uneven spacing, besides leaving the block length constant, one may also fix k. The connection to nonparametric regression and the smoothing problem (Section 4.3) is evident.

Henceforth we omit for convenience the prime and write {XOut(j)}m=1 on the process and {xOut(j)}m=1 on the sample level.

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