Let mn be defined as in Problem 12.2. Show that for every distribution of (X, Y ) which satisfies |X| bounded a.s., |Y | bounded a.s., and m (p, C)-smooth one has, for n sufficiently large,...


Let mn be defined as in Problem 12.2. Show that for every distribution of (X, Y ) which satisfies |X| bounded a.s., |Y | bounded a.s., and m (p, C)-smooth one has, for n sufficiently large,


                           E




|mn(x) − m(x)| 2 µ(dx)  ≤ c · C 2 2p+1 · log(n) 5 n 2p 2p+1 .



May 03, 2022
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