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

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10 Multivariate nonparametric estimation • Bias and variance functions are { 1 ∂ 2 m b α (x) = µ 2 (K) 2 ∂ 2 (x) + ∂m (x) ∂f } (x) f −1 (x) x α ∂x α ∂x α {∫ v(x) = σ 2 (x)f −1 (x) } d K 2 (u) du ST5207 Nonparametric Regression, 10th March 2005
11 Multivariate nonparametric estimation • Bias and variance functions are { 1 ∂ 2 m b α (x) = µ 2 (K) 2 ∂ 2 (x) + ∂m (x) ∂f } (x) f −1 (x) x α ∂x α ∂x α {∫ v(x) = σ 2 (x)f −1 (x) } 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) ST5207 Nonparametric Regression, 10th March 2005
Page 1 and 2: 1 ST5207 Nonparametric Regression,
Page 3 and 4: 3 Multivariate nonparametric estima
Page 9: 9 Multivariate nonparametric estima
Page 13 and 14: 13 Multivariate local linear estima
Page 23 and 24: 23 Computing and dimension reductio
Page 25 and 26: 25 Computing and dimension reductio

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

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