Extreme Values and the Multivariate Compact Law of the Iterated Logarithm

Steven J. Sepanski ()
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Steven J. Sepanski: Saginaw Valley State University

Journal of Theoretical Probability, 2001, vol. 14, issue 4, 989-1018

Abstract: Abstract For a sequence of independent identically distributed Euclidean random vectors, we prove a compact Law of the iterated logarithm when finitely many maximal terms are omitted from the partial sum. With probability one, the limiting cluster set of the appropriately operator normed partial sums is the closed unit Euclidean ball. The result is proved under the hypotheses that the random vectors belong to the Generalized Domain of Attraction of the multivariate Gaussian law and satisfy a mild integrability condition. The integrability condition characterizes how many maximal terms must be omitted from the partial sum sequence.

Keywords: law of the iterated logarithm; central limit theorem; generalized domain of attraction; extreme values; operator normalization; trimmed sums (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1017576903851

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