ON THE NORMAL APPROXIMATIONS OF STUDENTIZED U-STATISTIC
نویسندگان
چکیده
منابع مشابه
On normal approximations to U-statistics
Let X1, . . . ,Xn be i.i.d. random observations. Let S = L + T be a U -statistic of order k ≥ 2, where L is a linear statistic having asymptotic normal distribution, and T is a stochastically smaller statistic. We show that the rate of convergence to normality for S can be simply expressed as the rate of convergence to normality for the linear part L plus a correction term, (varT) ln(varT), und...
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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 mea...
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ژورنال
عنوان ژورنال: JOURNAL OF THE JAPAN STATISTICAL SOCIETY
سال: 1995
ISSN: 1882-2754,1348-6365
DOI: 10.14490/jjss1995.25.19