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Empirical Edgeworth Expansions for Symmetric Statistics
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Journal Article
Empirical Edgeworth Expansions for Symmetric Statistics
1998
Overview
In this paper the validity of a one-term Edgeworth expansion for Studentized symmetric statistics is proved. We propose jackknife estimates for the unknown constants appearing in the expansion and prove their consistency. As a result we obtain the second-order correctness of the empirical Edgeworth expansion for a very general class of statistics, including U-statistics, L-statistics and smooth functions of the sample mean. We illustrate the application of the bootstrap in the case of a U-statistic of degree two.
Publisher
Institute of Mathematical Statistics,The Institute of Mathematical Statistics
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