US-France Cooperative Research: The Asymptotic Behavior of Increment and Tail Processes

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This award will support collaborative research in statistics and probability between Dr. David Mason, University of Delaware and Professor Paul Deheuvels, Laboratory for Theoretical and Applied Statistics, University of Paris VI, France. The investigators will focus on the following areas: 1) increment processes, which include functional laws of the iterated logarithm for the increments of the empirical process, nonparametric function estimation and two sample Bahaduir-Kiefer test statistics, and 2) tail processes, which among other problems encompass statistical inference about the tails of a distribution and testing for outliers. Inference about the upper tail of a distribution has a large number of important applications, such as in insurance to estimate the probability of a large claim or in engineering to determine a reasonable safe height to construct a dam or oil platform. The two investigators are considered leading researchers in this area of mathematics and the proposed project will benefit from their complementary expertise and previous successful collaborative efforts.