Invariance principles for a multivariate Student process in the generalized domain of attraction of the multivariate normal law

Yuliya V. Martsynyuk

Statistics & Probability Letters, 2012, vol. 82, issue 12, 2270-2277

Abstract: 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.

Keywords: Uniform Euclidean norm approximation in probability; Functional central limit theorem (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2012.08.008

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