Laws of the iterated logarithm for partial sum processes indexed by functions |
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| Authors: | Michael Lacey |
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| Affiliation: | (1) University of Illinois at Urbana-Champaign, Champaign, USA;(2) Present address: Department of Statistics, University of North Carolina, 27599-3618 Chapel Hill, North Carolina |
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| Abstract: | We establish a bounded and a compact law of the iterated logarithm for partial sum processes indexed by classes of functions. We assume a growth condition on the metric entropy under bracketing. Examples show that our results are sharp. As a corollary we obtain new results for weighted sums of independent identically distributed random variables. |
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| Keywords: | Law of the iterated logarithm partial sum processes metric entropy |
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