Assume that a local averaging estimate is weakly universally consistent. Prove that (v) in Theorem 4.1 is satisfied (Stone XXXXXXXXXXHint: Consider the case m = 0 and Y ±1 valued. Prove the extension...

Assume that a local averaging estimate is weakly universally consistent. Prove that (v) in Theorem 4.1 is satisfied (Stone (1977)). Hint: Consider the case m = 0 and Y ±1 valued.

Prove the extension of Theorem 4.3 for rectangle partitions:

                Emn − m2 ≤ cˆ n 2d j=1 hnj + C2 d j=1 h2 nj .