Abstract
We present a method for deriving the limiting distribution of the maximum of a normed empirical moment generating function process indexed by one parameter. We first extend slightly the results of Csörgő et al. (1986b) to provide the rate of convergence for a Gaussian approximation to a non-Donsker empirical process. In cases we consider, the maximum tends to infinity in probability, but when appropriately scaled has a limiting Gumbel extreme value distribution.
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AMS 2000 Subject Classification
Primary—62E20, 60G70
*Author for correspondence: School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia.
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Stewart, M., Robinson, J. Extremes of Normed Empirical Moment Generating Function Processes. Extremes 6, 319–333 (2003). https://doi.org/10.1007/s10687-004-4723-1
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DOI: https://doi.org/10.1007/s10687-004-4723-1