On the pointwise central limit theorem and mixtures of stable distributions
I. Berkes and
E. Csáki
Statistics & Probability Letters, 1996, vol. 29, issue 4, 361-368
Abstract:
Let X1, X2, ... be i.i.d. r.v.'s with EX1 = 0. EX21 - 1 and put Sn = X1 + ... + Xn. We investigate the a.s. limiting behavior of for general norming sequences (ak). The pointwise central limit theorem shows that LN converges a.s. to the normal distribution if ak = [radical sign]k; in our paper we prove the surprising result that for suitably chosen (ak) the expression LN can converge also to non-Gaussian limits, in particular, any symmetric stable distribution is a possible limit of LN. We shall determine the class of limit distributions of LN and extend the result to the case when Xn belong to the domain of attraction of a stable law.
Keywords: Pointwise; central; limit; theorem; Stable; distributions; Mixtures (search for similar items in EconPapers)
Date: 1996
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