eprintid: 989
rev_number: 7
eprint_status: archive
userid: 36
dir: disk0/00/00/09/89
datestamp: 2011-10-31 15:04:57
lastmod: 2011-11-03 13:19:36
status_changed: 2011-10-31 15:04:57
type: article
metadata_visibility: show
creators_name: Crimaldi, Irene
creators_id: irene.crimaldi@imtlucca.it
title: Convergence results for a normalized triangular array of symmetric random variables
ispublished: pub
subjects: HA
subjects: QA
divisions: EIC
full_text_status: none
abstract: For a triangular array of symmetric random variables (without any integrability condition) we replace the classical assumption of row-wise independence by that of row-wise joint symmetry. Under this weaker assumption we prove some results concerning the convergence in distribution of a suitable sequence of randomly normalized sums to the standard normal distribution. Then we exhibit a class of row-wise independent triangular arrays for which the ordinary sums fail to converge in distribution, while our results enable us to affirm the convergence in distribution of the normalized sums.
date: 2002
date_type: published
publication: Expositiones mathematicae
volume: 20
number: 4
publisher: Elsevier
pagerange: 375-384
id_number: doi:10.1016/S0723-0869(02)80014-7
refereed: TRUE
issn: 0723-0869
official_url: http://dx.doi.org/10.1016/S0723-0869(02)80014-7
citation:   Crimaldi, Irene  Convergence results for a normalized triangular array of symmetric random variables.  Expositiones mathematicae, 20 (4).  pp. 375-384.  ISSN 0723-0869      (2002)