A U-statistic averages a symmetric function of distinct sample observations over all unordered -tuples. For independent and identically distributed observations it is an unbiased estimator of . Omitting repeated indices can remove diagonal contributions in quadratic plug-in estimators.
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A U-statistic is a type of statistic used in non-parametric statistical inference, particularly in estimating population parameters and testing hypotheses. It is designed to provide a way to estimate the value of a functional of a distribution based on a sample. U-statistics are particularly useful because they have desirable properties such as being asymptotically unbiased and having an asymptotic normal distribution. The general form of a U-statistic is constructed from a symmetric kernel function.