In this paper we prove the central limit theorem for Hotelling's T 2 statistic when the dimension of the random vectors is proportional to the sample size. © 2011 Institute of Mathematical Statistics.
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Pan, G. M., & Zhou, W. (2011). Central limit theorem for Hotelling’s t2 statistic under large dimension. Annals of Applied Probability, 21(5), 1860–1910. https://doi.org/10.1214/10-AAP742