Examples
Some examples: If the U-statistic is the sample mean.
If, the U-statistic is the mean pairwise deviation, defined for .
If, the U-statistic is the sample variance with divisor, defined for .
The third -statistic, the sample skewness defined for, is a U-statistic.
The following case highlights an important point. If is the median of three values, is not the median of values. However, it is a minimum variance unbiased estimate of the expected value of the median of three values and in this application of the theory it is the population parameter defined as "the expected value of the median of three values" which is being estimated, not the median of the population. Similar estimates play a central role where the parameters of a family of probability distributions are being estimated by probability weighted moments or L-moments.
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