Empirical Edgeworth expansions for symmetric statistics
Open Access
- 1 August 1998
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 26 (4) , 1540-1569
- https://doi.org/10.1214/aos/1024691253
Abstract
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.Keywords
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