Show that the error probability of the plug-in decision rule (1.9) satisfies 0 ≤ P{gn(X) = Y |Dn} − P{g∗(X) = Y } ≤ M k=1 Rd |m(k) n (x) − m(k) (x)|µ(dx) ≤ M k=1 Rd |m(k) n (x) − m(k) (x)| 2 µ(dx) 1...

Show that the error probability of the plug-in decision rule (1.9) satisfies 0 ≤ P{gn(X) = Y |Dn} − P{g∗(X) = Y } ≤ M k=1 Rd |m(k) n (x) − m(k) (x)|µ(dx) ≤ M k=1

Rd |m(k) n (x) − m(k) (x)| 2 µ(dx) 1 2 .

May 23, 2022