On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics

DOI10.1007/BF00319104zbMath0629.62019OpenAlexW2049548185MaRDI QIDQ1094021

John H. J. Einmahl, David M. Mason, Erich Haeusler

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00319104

zbMATH Keywords

characterizationalmost sure stability of weighted empirical distribution functionsdomain of attraction of a non-normal stable lawstandardized uniform empirical distributionsums of order statistics

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Characterization and structure theory of statistical distributions (62E10)

Related Items

A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games ⋮ Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean ⋮ On the standarized empirical process

Cites Work

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• The asymptotic distribution of sums of extreme values from a regularly varying distribution
• A law of the iterated logarithm for sums of extreme values from a distribution with a regularly varying upper tail
• Strong limit theorems for weighted quantile processes
• Bounds for weighted empirical distribution functions
• Linear bounds on the empirical distribution function
• Relative stability of trimmed sums
• The strong law of large numbers when extreme terms are excluded from sums
• The law of the iterated logarithm for normalized empirical distribution function
• Stability for sums of i.i.d. random variables when extreme terms are excluded
• A Note on a Paper of Barnes and Tucker
• Regularly varying functions

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