Convergence results for a normalized triangular array of symmetric random variables |
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Authors: | Irene Crimaldi |
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Institution: | Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
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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. |
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