1 2 (U (2) n ) 2 defined in XXXXXXXXXXis equal to the sample variance (unbiased form) and is an optimal nonparametric estimator of the functional T2(F) = R R1 R R1 (x1 − x2) 2/2dF(x1)dF(x2) = σ 2 F ....

1 2 (U (2) n ) 2 defined in (3.64) is equal to the sample variance (unbiased form) and is an optimal nonparametric estimator of the functional T2(F) = R R1 R R1 (x1 − x2) 2/2dF(x1)dF(x2) = σ 2 F . Verify that 1 2 (U (2) n ) 2 is a Ustatistic with a kernel of degree 2.