Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law
Assuming that the sample correlation matrix of vector X converges to a positive definite nonstochastic matrix, we establish a uniform Euclidean norm approximation in probability and a functional CLT for a multivariate Student process, based on independent copies of X. These results obtain if and only if X is in the generalized domain of attraction of the multivariate normal law.
Volume (Year): 82 (2012)
Issue (Month): 12 ()
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