The Annals of Probability
- Ann. Probab.
- Volume 37, Number 6 (2009), 2174-2199.
On normal approximations to U-statistics
Let X1, …, Xn be i.i.d. random observations. Let be a U-statistic of order k≥2 where is a linear statistic having asymptotic normal distribution, and is a stochastically smaller statistic. We show that the rate of convergence to normality for can be simply expressed as the rate of convergence to normality for the linear part plus a correction term, , under the condition . An optimal bound without this log factor is obtained under a lower moment assumption for . Some other related results are also obtained in the paper. Our results extend, refine and yield a number of related-known results in the literature.
Ann. Probab., Volume 37, Number 6 (2009), 2174-2199.
First available in Project Euclid: 16 November 2009
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62E20: Asymptotic distribution theory
Bentkus, Vidmantas; Jing, Bing-Yi; Zhou, Wang. On normal approximations to U -statistics. Ann. Probab. 37 (2009), no. 6, 2174--2199. doi:10.1214/09-AOP474. https://projecteuclid.org/euclid.aop/1258380786