Cramér Type Moderate Deviations for Studentized U-statistics
نویسندگان
چکیده
The U-statistic elegantly and usefully generalizes the notion of a sample mean. Typical examples include (i) sample mean: h(x1, x2) = 12 (x1 + x2); (ii) sample variance: h(x1, x2) = 12 (x1 − x2); (iii) Gini’s mean difference: h(x1, x2) = |x1 − x2|; (iv) one-sample Wilcoxon’s statistic: h(x1, x2) = 1(x1 + x2 ≤ 0). The non-degenerate U-statistic shares many limiting properties with the sample mean. For example, if Eh(X1, X2) < ∞ and σ 1 = Var(g(X1)) > 0, where
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