TY  - JOUR
VL  - 20
ID  - eprints989
EP  - 384
PB  - Elsevier
SN  - 0723-0869
A1  - Crimaldi, Irene
N2  - 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.
SP  - 375
Y1  - 2002///
TI  - Convergence results for a normalized triangular array of symmetric random variables
AV  - none
IS  - 4
JF  - Expositiones mathematicae
UR  - http://dx.doi.org/10.1016/S0723-0869(02)80014-7
ER  -