Prove that the Nadaraya–Watson kernel estimate defined by (2.2) satisfies (2.4). Hint: Let mn(x) be the Nadaraya–Watson kernel estimate. Show that, for any c ∈ R, n i=1 K x − Xi h  (Yi − c) 2 = n i=1...

Prove that the Nadaraya–Watson kernel estimate defined by (2.2) satisfies (2.4).

Hint: Let mn(x) be the Nadaraya–Watson kernel estimate. Show that, for any c ∈ R,

n i=1 K x − Xi h  (Yi − c) 2

= n i=1 K x − Xi h  (Yi − mn(x))2 + n i=1 K x − Xi h  (mn(x) − c) 2 .