On normal approximations to U-statistics
نویسنده
چکیده
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), under the condition
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