Comparative study on rate of convergence to normal distribution for u-statistics and method of moments estimator for population variance.

In this dissertation, we examine the small and large sample properties of the U-statistics (Un) for an estimable parameter : For small sample, Un is found to be MVUE and Su cient. Large sample properties of Un examined are Consistency and Asymptotic normality. We also compare the rate of convergence to normal distribution between the U-statistics and the method of moments estimator for the population variance. Berry-Esseen bound for U- statistics of order 2 is given and the results are used to nd the rate of convergence to normal for the U-statistics for the population variance. Berry-Esseen bound for S2 the method of
moments estimator for the population variance is also given. Method of moments estimator is found to converge faster to normality than the U-statistics. Finally, we review the di erent proofs of Hoe ding's one sample U-statistics theorem as given in the period 1948-2012.