A bounded \(N\)-tuplewise independent and identically distributed counterexample to the CLT

DOI10.1007/s004400050170zbMath0910.60008OpenAlexW1983634614WikidataQ124830714 ScholiaQ124830714MaRDI QIDQ1265412

Alexander R. Pruss

Publication date: 19 April 1999

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

Full work available at URL: https://doi.org/10.1007/s004400050170

zbMATH Keywords

counterexamplecentral limit theorem\(N\)-tuplewise independencequadruplewise independence

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (9)

On the central limit theorem for negatively correlated random variables with negatively correlated squares. ⋮ Concentration inequalities and limit theorems for randomized sums ⋮ A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables ⋮ An example of a stationary, triplewise independent triangular array for which the CLT fails ⋮ WLLN for arrays of nonnegative random variables ⋮ On a stationary, triple-wise independent, absolutely regular counterexample to the central limit theorem ⋮ A strictly stationary, \(N\)-tuplewise independent counterexample to the central limit theorem ⋮ Counterexamples to the classical central limit theorem for triplewise independent random variables having a common arbitrary margin ⋮ Non-uniform Berry-Esseen bounds for coordinate symmetric random vectors with applications

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