Lecture7 Slide - The Department of Statistics and Applied Probability ...
Lecture7 Slide - The Department of Statistics and Applied Probability ...
Lecture7 Slide - The Department of Statistics and Applied Probability ...
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16<br />
Multivariate local linear estimation<br />
• Separately, the estimators are (α = 1, ..., d)<br />
ˆm (x) = e T 0<br />
(<br />
X T WX ) −1<br />
X T WY, e T 0 = (1, 0, ..., 0)<br />
̂∂m<br />
∂x α<br />
(x) = e T α<br />
(<br />
X T WX ) −1<br />
X T WY, e T α = (0, 0, ..., 0, 1, 0..., 0)<br />
• Corresponding functions are (α = 1, ..., d)<br />
m (x) = m (x) e T (<br />
0 X T WX ) −1<br />
X T WXe 0<br />
∂m<br />
(x) = ∂m (x) e T (<br />
α X T WX ) −1<br />
X T WXe α<br />
∂x α ∂x α<br />
ST5207 Nonparametric Regression, 10th March 2005
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