=+14.15. This exercise involves some of the details in Example 14.8.

(i) Show that the functional θ is a special case of (14.48).

(ii) Verify that θ(Fn) = n−2 n i=1

n j=1 1(Xi+Xj>0), which is a V -statistic.

(iii) Verify (14.51) and (14.52) and thus conclude that the asymptotic conditional distribution of √n(U∗

n − Un) given X1,...,Xn is the same as the asymptotic distribution of √n(Un − θ).

(iv) What is the asymptotic distribution of √n(Un − θ)?