Lecture3 Slide - The Department of Statistics and Applied Probability ...

6
Step one, continued
• E |ξ in | 2 [
= n −2 E |K h (X i − x) − EK h (X i − x)| 2
= n −2 E {K h (X i − x)} 2 − {EK h (X i − x)} 2]
•
E {K h (X i − x)} 2 =
•
= 1 h 2 ∫
= f (x)
h
σ 2 in = f (x)
n 2 h
∫
K 2 h (u − x) f (u) du = 1 h 2 ∫
K 2 (v) f (x + hv) hdv = 1 h
∫
∫
K 2 (v) dv + 1 f (x)
u (h) =
h h
K 2 (v) dv {1 + u (1)} , V 2 n = f (x)
nh
∫
K 2 ( u − x
h
K 2 (v) f (x + hv) dv
∫
K 2 (v) dv + u (1)
∫
)
f (u) du
K 2 (v) dv {1 + u (1)}
ST5207 Nonparametric Regression, 27th January 2005