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Sample Path Large Deviations for Order Statistics
Published online by Cambridge University Press: 14 July 2016
Abstract
We consider the sample paths of the order statistics of independent and identically distributed random variables with common distribution function F. If F is strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the Skorokhod M1 topology. Sanov's theorem is deduced in the Skorokhod M'1 topology as a corollary to this result. A number of illustrative examples are presented, including applications to the sample paths of trimmed means and Hill plots.
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- Research Article
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- Copyright © Applied Probability Trust 2011
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