Asymptotic Results for Spacings of Largest Order Statistics

Arvydas Astrauskas ()
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Arvydas Astrauskas: Institute of Data Science and Digital Technologies, Vilnius University

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 1, No 3, 65-95

Abstract: Abstract We prove o- and O-type asymptotic results in probability for properly normalized spacings (differences) of the largest order statistics based on i.i.d. random sample, as the size of the sample tends to infinity. In particular, compactness properties of sequences of spacings are investigated. These results are applied to study the corresponding asymptotic properties of the ratios of upper order statistics and the number of observations near extremes. A common distribution function of the sample is assumed to satisfy mild conditions on regular variation at its right endpoint.

Keywords: Spacings; extreme order statistics; stochastic boundedness and compactness; limit theorems; number of near-extremes; regular variation; 60G70; 62G32; 26A12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-024-00340-2

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