# DMtutorial8s - Tutorial 9 solutions 1 Suppose we need to...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Tutorial 9: solutions 1. Suppose we need to estimate a varying coefficient model Y = a ( x 1 ) + a 1 ( x 2 ) x 3 + ε with sample ( x i 1 , ..., x i 3 , Y i ) , i = 1 , ..., n . Using cubic spline to approximate a k ( z ). (a) write the expression for the estimator of a 1 ( z ) (b) find the 95% confidence band for a 1 ( x ). (a) Suppose we choose t 1 ,...,t J as knots for a ( . ) and thus we have approximately a ( x ) = J +4 X j =1 θ j B j ( x ) where base funcitons B 1 ( x ) = 1 ,B 2 ( x ) = x,..., B J +4 ( x ) = ( x- t J ) 3 + . Suppose we choose t 1 ,...,t J 1 as knots for a 1 ( . ) and thus we have approximately a 1 ( x ) = J 1 +4 X j =1 γ j B j ( x ) where base funcitons B 1 ( x ) = 1 ,B 2 ( x ) = x,..., B J 1 +4 ( x ) = ( x- t J 1 ) 3 + . The model is now Y = J +4 X j =1 θ j B j ( x ) + J 1 +4 X j =1 γ j { B j ( x ) x 1 } + ε or Y = β > W + ε where β = ( θ 1 ,...,θ J +4 ,γ 1 ,...,γ J 1 +4 ) and W = ( B 1 ( x 1 ) ,...,B J +4 ( x 1 ) ,B 1 ( x 2 ) x 3 ,...,B J +4 ( x 2 )...
View Full Document

## 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.

### Page1 / 2

DMtutorial8s - Tutorial 9 solutions 1 Suppose we need to...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online