The rates of convergence to the normal distribution are investigated for U-statistics of degree two. We derive an inequality which gives a lower bound for the uniform distance between the distribution of a U-statistic and the standard normal distribution, and which is useful in the case where the distribution of U-statistic is symmetric around the origin. The proof is based on Stein's method.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics