Lecture7 Slide - The Department of Statistics and Applied Probability ...

12
Multivariate nonparametric estimation
• Bias and variance functions are
{ 1
b α (x) = µ 2 (K)
2
{∫
v(x) = σ 2 (x)f −1 (x)
∂ 2 m
∂ 2 (x) + ∂m (x) ∂f (x) f −1 (x)
x α ∂x α ∂x α
} d
K 2 (u) du
• The local linear estimator (to be discussed next) has limiting
distribution of the same form, but with
b α (x) = µ 2 (K) 1 2
∂ 2 m
∂ 2 x α
(x)
• The local linear weighted least squares problem is
n∑ {
2
{ ˆm (x) , ∇m (x)} = arg min Y i − a − (X i − x) b} T wi (x)
a,b
i=1
}
ST5207 Nonparametric Regression, 10th March 2005