On the locations of maxima and minima in a sequence of exchangeable random variables

Ferger, D.

doi:10.1090/tpms/1154

Author: D. Ferger
Journal: Theor. Probability and Math. Statist. 105 (2021), 35-50
MSC (2020): Primary 60G70; Secondary 62E15
DOI: https://doi.org/10.1090/tpms/1154
Published electronically: December 7, 2021
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Abstract: We show for a finite sequence of exchangeable random variables that the locations of the maximum and minimum are independent from every symmetric event. In particular they are uniformly distributed on the grid without the diagonal. Moreover, for an infinite sequence we show that the extrema and their locations are asymptotically independent. Here, in contrast to the classical approach we do not use affine-linear transformations. Moreover it is shown how the new transformations can be used in extreme value statistics.

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