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A Berry-Esseen bound for symmetric statistics. (English) Zbl 0525.62023

MSC:
62E20 Asymptotic distribution theory in statistics
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[1] Bickel, P.J.: Edgeworth expansions in nonparametric statistics. Ann. Statist. 2, 1-20 (1974) · Zbl 0284.62018
[2] Callaert, H., Janssen, P.: The Berry-Esseen theorem for U-statistics. Ann. Statist. 6, 417-421 (1978) · Zbl 0393.60022
[3] Chan, Y.-K., Wierman, J.: On the Berry-Esseen theorem for U-statistics, Ann. Probability 5, 136-139 (1977) · Zbl 0381.60022
[4] Efron, B., Stein, C.: The jackknife estimate of variance, Ann. Statist. 9, 586-596 (1981) · Zbl 0481.62035
[5] Feller, W.: An Introduction to Probability Theory and Its Applications. Vol. II, 2nd Ed. New York: Wiley 1971 · Zbl 0219.60003
[6] Helmers, R.: A Berry-Esseen theorem for linear combinations of order statistics. Ann. Probability 9, 342-347 (1981) · Zbl 0474.62039
[7] Helmers, R.: Edgeworth Expansions for Linear Combinations of Order Statistics. Mathematical Centre Tracts 105. Mathematisch Centrum, Amsterdam (1982) · Zbl 0485.62017
[8] Helmers, R., Van Zwet, W.R.: The Berry-Esseen bound for U-statistics. Statistical Decision Theory and Related Topics, III Vol. 1, S.S. Gupta and J.O. Berger (eds.), 497-512. New York: Academic Press 1982
[9] Hoeffding, W.: A class of statistics with asymptotically normal distributions. Ann. Math. Statist. 19, 293-325 (1948) · Zbl 0032.04101
[10] Hoeffding, W.: The strong law of large numbers for U-statistics. Inst. of Statist., Univ. of North Carolina, Mimeograph Series No. 302 (1961) · Zbl 0211.20605
[11] Karlin, S., Rinott, Y.: Applications of ANOVA type decompositions for comparisons of conditional variance statistics including jackknife estimates. Ann. Statist. 10, 485-501 (1982) · Zbl 0491.62036
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