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

29
Digression to density estimation
From ˆf (x) − f (x) = n ∑
i=1
ξ in + Bias
{
ˆf (x)
}
, one gets
E
{
{ } 2 n
} 2
∑
{ }
ˆf (x) − f (x) = E ξ in +Bias 2 ˆf (x)
i=1
= V 2 n +Bias 2 { ˆf (x)
}
E
{ } { 2 f (x)
f ˆf (2) (x) − f (x) =
nh c (x)
K {1 + u (1)}+ h 2 d K + u ( h 2)} 2
2!
ST5207 Nonparametric Regression, 27th January 2005