Lecture3 Slide - The Department of Statistics and Applied Probability ...
Lecture3 Slide - The Department of Statistics and Applied Probability ...
Lecture3 Slide - The Department of Statistics and Applied Probability ...
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19<br />
Step one, continued<br />
• E |K h (X i − x)| 2+δ ≤ 1<br />
h 1+δ<br />
|EK h (X i − x)| 2+δ =<br />
max f (t) ∫ K 2+δ (v) dv<br />
t∈[a,b]<br />
{ }<br />
∣<br />
∣Bias ˆf (x)<br />
+ f (x) ∣ 2+δ = f (x) 2+δ +u ( h 2)<br />
E |ξ in | 2+δ ≤ n −(2+δ) 2 1+δ 1<br />
h 1+δ<br />
∫<br />
max f (t)<br />
t∈[a,b]<br />
K 2+δ (v) dv {1 + u (1)}<br />
•<br />
=<br />
V −(2+δ)<br />
n<br />
[ f (x)<br />
nh<br />
∫<br />
n∑<br />
i=1<br />
E |ξ in | 2+δ = V −(2+δ)<br />
n nE |ξ in | 2+δ<br />
] −(2+δ)/2<br />
K 2 (v) dv {1 + u (1)} nE |ξ in | 2+δ<br />
ST5207 Nonparametric Regression, 27th January 2005
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