U-statistic

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In statistical theory, a U-statistic is a specific type of estimator defined in a particular way. The usefulness of the concept in statistical theory is that it allows a minimum-variance unbiased estimator to be derived from any unbiased estimator.

Suppose that a problem involves Independent and identically-distributed random variables and that estimation of a certain parameter is required. Suppose that a simple unbiased estimate can be constructed based on only a few observations: this defines the basic estimator based on a given number of observations. For example, a single observation is itself an unbiased estimate of the mean and a pair of observations can be used to derive an unbiased estimate of the variance. The U-statistic based on this estimator is defined as the average (across all combinatorial selections of the given size from the full set of observations) of the basic estimator applied to the sub-samples.

[edit] References

Lee, A.J. (1990) U-Statistics: Theory and Practice. Marcewl Dekker, New York. pp320 ISBN 0824782534