Convergence in distribution of lightly trimmed and untrimmed sums are equivalent

DOI10.1017/S0305004100076246zbMath0787.60026MaRDI QIDQ4272605

Harry Kesten

Publication date: 19 May 1994

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

convergence in distributionlight trimming

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (10)

Tightness and convergence of trimmed Lévy processes to normality at small times ⋮ ASYMPTOTIC BEHAVIOR OF TRIMMED SUMS ⋮ Random deletion does not affect asymptotic normality or quadratic negligibility ⋮ Trimmed stable AR(1) processes ⋮ Prime numbers in typical continued fraction expansions ⋮ Mean convergence for intermediately trimmed Birkhoff sums of observables with regularly varying tails ⋮ The central limit theorem for sums of trimmed variables with heavy tails ⋮ Convergence of trimmed Lévy processes to trimmed stable random variables at 0 ⋮ Strong laws of large numbers for intermediately trimmed sums of i.i.d. random variables with infinite mean ⋮ Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean

Cites Work

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• A probabilistic approach to the asymptotic distribution of sums of independent, identically distributed random variables
• The Extreme Terms of a Sample and Their Role in the Sum of Independent Variables
• The strong law of large numbers when extreme terms are excluded from sums
• Stability for sums of i.i.d. random variables when extreme terms are excluded
• On the Extreme Terms of a Sample From the Domain of Attraction of a Stable Law
• On the concentration function of a sum of independent random variables
• The Influence of the Maximum Term in the Addition of Independent Random Variables

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