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Cramér type moderate deviations for trimmed \(L\)-statistics. (English) Zbl 1362.60024

Summary: We establish Cramér type moderate deviation results for heavy trimmed \(L\)-statistics; we obtain our results under a very mild smoothness condition on the inversion \(F^{-1}\) (\(F\) is the underlying distribution function of i.i.d. observations) near two points, where trimming occurs, we assume also some smoothness of weights of the \(L\)-statistic. Our results complement previous work on Cramér type large deviations for trimmed \(L\)-statistics [{the author, “Cramér type large deviations for trimmed \(L\)-statistics”, Probab. Math. Stat. (to appear); H. Callaert et al., Commun. Stat., Theory Methods 11, 2689–2698 (1982; Zbl 0503.62020)].}

MSC:

60F10 Large deviations
62G30 Order statistics; empirical distribution functions
62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness

Citations:

Zbl 0503.62020
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References:

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