Annals of Applied Probability

Central limit theorem for Hotelling’s T2 statistic under large dimension

G. M. Pan and W. Zhou

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In this paper we prove the central limit theorem for Hotelling’s T2 statistic when the dimension of the random vectors is proportional to the sample size.

Article information

Ann. Appl. Probab., Volume 21, Number 5 (2011), 1860-1910.

First available in Project Euclid: 25 October 2011

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Mathematical Reviews number (MathSciNet)

Primary: 15B52: Random matrices 60F15: Strong theorems 62E20: Asymptotic distribution theory
Secondary: 60F17: Functional limit theorems; invariance principles

Hotelling’s T2 statistic sample means sample covariance matrices central limit theorem Stieltjes transform


Pan, G. M.; Zhou, W. Central limit theorem for Hotelling’s T 2 statistic under large dimension. Ann. Appl. Probab. 21 (2011), no. 5, 1860--1910. doi:10.1214/10-AAP742.

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