High Quality Content by WIKIPEDIA articles! In statistical theory, a U-statistic is a class of statistics that is especially important in estimation theory. In elementary statistics, U-statistics arise naturally in producing minimum-variance unbiased estimators. A mean-unbiased estimator that is conditioned on the order statistics (of an sequence of independent and identically distributed random variables) becomes the minimum-variance unbiased estimator, by the Rao-Blackwell theorem. Of even more importance is that the theory related to U-statistics allows a single theoretical framework to be used in non-parametric statistics to prove results for a wide range of test-statistics and estimators relating to the asymptotic normality and to the variance (in finite samples) of such quantities. In addition the theory has applications to estimators which are not themselves U-statistics.