Assume that the weights {Wn,i} are nonnegative and the estimate is weakly universally consistent. Prove that (i) in Theorem 4.1 is satisfied (Stone XXXXXXXXXXHint: Apply Problem 4.1 for...

Assume that the weights {Wn,i} are nonnegative and the estimate is weakly universally consistent. Prove that (i) in Theorem 4.1 is satisfied (Stone (1977)). Hint: Apply Problem 4.1 for

                               Y = f(X) = m(X),

and show that

                      lim n→∞  E  n i=1 |Wn,i(X)|f(Xi)  − Ef(X) 2 = 0.