An extension of almost sure central limit theory

Siegfried Hörmann

Statistics & Probability Letters, 2006, vol. 76, issue 2, 191-202

Abstract: We show that if Xn are i.i.d. random variables with and (dk) is a positive numerical sequence obeying a condition similar to Kolmogorov's condition for the LIL, then letting we haveThis shows that logarithmic means, used traditionally in a.s. central limit theory, can be replaced by other means lying much closer to ordinary (Cesàro) averages, leading to considerably sharper results. Our results remain valid (under suitable regularity conditions) for independent random variables Xn satisfying the weak limit theorem with an arbitrary distribution function H.

Keywords: Almost; sure; central; limit; theorem; Summation; methods (search for similar items in EconPapers)
Date: 2006
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