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

12
Step one, continued
• E |ξ in | 2+δ = n −(2+δ) E |K h (X i − x) − EK h (X i − x)| 2+δ
• E |ξ in | 2+δ ≤ n −(2+δ) E {|K h (X i − x)| + |EK h (X i − x)|} 2+δ
• Using (a + b) p ≤ 2 p−1 (a p + b p ) , a, b > 0, p ≥ 1
E |ξ in | 2+δ ≤ n −(2+δ) 2 1+δ E
{|K h (X i − x)| 2+δ + |EK h (X i − x)| 2+δ}
•
E |K h (X i − x)| 2+δ =
= 1
h 2+δ ∫
∫
K 2+δ
h
K 2+δ ( u − x
h
(u − x) f (u) du
)
f (u) du
ST5207 Nonparametric Regression, 27th January 2005