Suppose (X1, Y1), . . . , (Xn, Yn) are i.i.d. P, with E(X2 i ) < ∞ and E(Y 2 i ) < ∞. The parameter of interest is θ(P) = Cov(Xi, Yi). Find a kernel for which the corresponding U-statistic Un is an unbiased estimator of θ(P). Under an appropriate moment assumption, find the limiting distribution of Un. Hint: Compute E[(X1 − X2)(Y1 − Y2)].