DMtutorial5s - Tutorial 6: suggested solutions 1. Suppose m...

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Unformatted text preview: Tutorial 6: suggested solutions 1. Suppose m ( x 1 , ..., x p ) = φ ( α 1 x 1 + ... + α p x p ). Prove that ∂m ( x 1 ,...,xp ) ∂x 1 ∂m ( x 1 ,...,xp ) ∂x 2 ... ∂m ( x 1 ,...,xp ) ∂xp = φ ( α 1 x 1 + ... + α p x p ) α 1 α 2 ... α p proof: Because ∂m ( x 1 , ..., x p ) ∂x k = φ ( α 1 x 1 + ... + α p x p ) α k 2. For a single-index model Y = φ ( α > X ) + ε . Suppose ( X i , y i ) are the observations and the estimator for α is ˆ α . For a new point X , predict the expectation of response using local linear kernel smoothing. the prediction value is ˆ g (ˆ α > X ) = ∑ n i =1 { s n, 2 (ˆ α > X ) K h (ˆ α > ( X i- X ))- s n, 1 (ˆ α > X ) K h (ˆ α > ( X i- X ))ˆ α > ( X i- X ) /h } Y i s n, 2 (ˆ α > X ) s n, (ˆ α > X )- s 2 n, 1 (ˆ α > X ) where s n,k (ˆ α > X ) n X i =1 K h (ˆ α > ( X i- X )) { ˆ α > ( X i- X ) /h } k , k = 0 , 1 , 2 3. For the ozone concentration...
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This note was uploaded on 10/04/2010 for the course STAT ST4240 taught by Professor Xiayingcun during the Fall '09 term at National University of Singapore.

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DMtutorial5s - Tutorial 6: suggested solutions 1. Suppose m...

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