Bounds for the Concentration of Asymptotically Normal Statistics |
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| Authors: | I. B. Alberink V. Bentkus |
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| Affiliation: | (1) Department of Mathematics, University of Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands, e-mail;(2) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany. e-mail |
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| Abstract: | ![]()
Let X1,..., Xn be independent, not necessarily identically distributed random variables. An optimal bound is derived for the concentration function of an arbitrary real-valued statistic T = T (X1,...,Xn) for which ET2 <  . Applications are given for Wilcoxon"s rank-sum statistic, U-statistics, Student"s statistic, the two-sample Student statistic and linear regression. |
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| Keywords: | concentration function non-i.i.d. sampling nonsymmetric and symmetric statistics U-statistics Wilcoxon" s rank-sum test (two-sample) Student" s statistic linear regression |
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