Almost sure versions of distributional limit theorems for certain order statistics.

DOI10.1016/S0167-7152(02)00156-6zbMath1033.60042OpenAlexW2046877316MaRDI QIDQ1871244

Ulrich Stadtmüller

Publication date: 7 May 2003

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(02)00156-6

zbMATH Keywords

intermediate order statisticsalmost sure limit theoremslogarithmic meanscentral order statistics

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (14)

Almost sure limit theorem for the order statistics of stationary Gaussian sequences ⋮ ALMOST SURE CENTRAL LIMIT THEOREMS OF THE PARTIAL SUMS AND MAXIMA FROM COMPLETE AND INCOMPLETE SAMPLES OF STATIONARY SEQUENCES ⋮ Some distributional limit theorems for the maxima of Gaussian vector sequences ⋮ Almost sure central limit theorem for the location and height of extreme order statistics and high values ⋮ Some applications of the Archimedean copulas in the proof of the almost sure central limit theorem for ordinary maxima ⋮ An extension of almost sure central limit theorem for order statistics ⋮ The almost sure central limit theorems for the maxima of sums under some new weak dependence assumptions ⋮ Almost sure convergence of extreme order statistics ⋮ Almost sure limit theorems for the maxima of some strongly dependent Gaussian sequences ⋮ On the universal a.s. central limit theorem ⋮ Almost sure max-limits for nonstationary Gaussian sequence ⋮ Almost sure central limit theorem for exceedance point processes of stationary sequences ⋮ On the almost sure convergence of randomly indexed maximum of random variables ⋮ Almost sure convergence for non-stationary random sequences

Cites Work

• On almost sure max-limit theorems
• A note on the almost sure central limit theorem
• Extremes and related properties of random sequences and processes
• An extension of the almost sure max-limit theorem
• A strong invariance principle for the logarithmic average of sample maxima.
• A universal result in almost sure central limit theory.
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Almost Sure Convergence in Extreme Value Theory
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