Empirical Edgeworth expansions for symmetric statistics. (English) Zbl 0929.62013
Summary: 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.
MSC:
| 62E20 | Asymptotic distribution theory in statistics |
| 62G09 | Nonparametric statistical resampling methods |
| 60F05 | Central limit and other weak theorems |
References:
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