Let Fn be a class of functions f : Rd → R and define the estimator mn by                              mn(·) = arg min f∈Fn 1 n n i=1 |f(Xi) − Yi| 2 .  Assume EY 2                            inf...

Let Fn be a class of functions f : Rd → R and define the estimator mn by

                             mn(·) = arg min f∈Fn 1 n n i=1 |f(Xi) − Yi| 2 .

 Assume EY 2 <>

                           inf f∈Fn  |f(x) − m(x)| 2 µ(dx) → 0 (n → ∞)

and

                             sup f∈Fn 1 n n i=1 |f(Xi) − TLYi| 2 − E  |f(X) − TLY | 2 → 0 (n → ∞) a.s.

for all L > 0 imply

                                     |mn(x) − m(x)| 2 µ(dx) → 0 (n → ∞) a.s.