The usual sample variance s2 is a u -statistic of order 2, Ask an Expert

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The usual sample variance s2 is a U -statistic of order 2. For n = 4, (X1 + X2 - X3 - X4)2/4 is another possible estimator of variance. Show that it is an unbiased estimator of the variance of X1 but that its variance is larger than that of s2, at least when the i.i.d. Xi have a normal distribution. Hint: If X has a standard normal N (0, 1) distribution, then EX 3 = 0 and EX 4 = 3.

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