The logarithmic average of sample extremes is asymptotically normal

Geostatistics of Dependent and Asymptotically Independent Extremes

Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, ...

The Mahonian Probability Distribution on Words Is Asymptotically Normal

The Mahonian statistic is the number of inversions in a permutation of a multiset with ai elements of type i, 1 ≤ i ≤ m. The counting function for this statistic is the q analog of the multinomial coefficient ( a1+···+am a1,...am ) , and the probability generating function is the normalization of the latter. We give two proofs that the distribution is asymptotically normal. The first is compute...

Smoothing sample extremes: The mixed model approach

Robust sample average approximation

Sample average approximation (SAA) is a widely popular approach to data-driven decisionmaking under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA’s tractability and asy...

Assessing when a sample is mostly normal

The use of trimming procedures constitutes a natural approach to robustifying statistical methods. This is the case of goodness-of-fit tests based on a distance, which can be modified by choosing trimmed versions of the distributions minimizing that distance. In this paper we consider the L2-Wasserstein distance and introduce the trimming methodology for assessing when a data sample can be cons...