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Media type:
E-Article
Title:
A Remark on Convergence in Distribution of U-Statistics
Contributor:
Gine, Evarist;
Zinn, Joel
imprint:
Institute of Mathematical Statistics, 1994
Published in:The Annals of Probability
Language:
English
ISSN:
0091-1798
Origination:
Footnote:
Description:
<p>It is proved that, for h measurable and symmetric in its arguments and X<sub>i</sub>i.i.d., if the sequence {n<sup>-m/2</sup>∑<sub>i<sub>1</sub>,...,i<sub>m</sub>≤ n,i<sub>j</sub>≠ i<sub>k</sub>if j≠ k</sub>h(X<sub>i<sub>1</sub>
</sub>,..., X<sub>i<sub>m</sub>
</sub>)}<sup>∞</sup>
<sub>n=1</sub>is stochastically bounded, then<tex-math>$Eh^2 < \infty$</tex-math>and Eh(X<sub>1</sub>,x<sub>2</sub>,...,x<sub>m</sub>) = 0 a.s.</p>