Necessary and Sufficient Condition for Asymptotic Normality of Standardized Sample Means

Abstract

The double sequence of standardized sample means constructed from an infinite sequence of square integrable independent random vectors in the plane with identically distributed coordinates is jointly asymptotically Normal if and only if the Cesaro means of the sequence of cross sample correlation coefficients converges to 0.

arXiv admin note: text overlap with arXiv:1612.01668