Limiting theorems for large dimensional sample means, sample covariance matrices and Hotelling's T2 statistics
Seminar Room 1, Newton Institute
It is well known that sample means and sample covariance matrices are independent if the samples are from the Gaussian distribution and are i.i.d.. In this talk, via investigating the random quardratic forms involving sample means and sample covariance matrices, we suggest the conjecture that the sample means and the sample covariance matrices under general distribution functions are asymptotically independent in the large dimensional case when the dimension of the vectors and the sample size both go to infinity with their ratio being a positive constant. As a byproduct, the central limit theorem for the Hotelling $T^2$ statistic under the large dimensional case is established.
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