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Unformatted text preview: Tutorial 4: Suggested solutions 1. comparing the estimators on the top of page 4 (chapter 2 part 1 ) and (2.3) on page 3 of part 2. Explain why there is not weight function in the estimator of page 4. Because the estimation on the top of page 2 (chapter 2 part 1 ) is to estimate a global parameter, we don’t need to estimate them locally. 2. Based on the notation in Lecture note (Chapter 2, part 2), eqns between (2.2) and (2.3), prove (2.3) First, we prove that for any Y and X , then the solution to minimize ( Y X β ) > ( Y X β ) with respect to β is ˆ β = ( X > X ) 1 X > Y (1) Write ( Y X β ) > ( Y X β ) = ( Y X ˆ β + X ˆ β X β ) > ( Y X ˆ β + X ˆ β X β ) = { ( I X ( X > X ) 1 X ) Y X ( ˆ β β ) } > { ( I X ( X > X ) 1 X ) Y X ( ˆ β β ) } = Y > ( I X ( X > X ) 1 X ) Y + ( ˆ β β ) > X > X ( ˆ β β ) Therefore, the minimum point achieved when the second term is 0, i.e. β = ˆ β Let β = ( a ,a 1 ,...,a q ,b ,...,b q ) > . Because n X i =1 { Y i [ a + a 1 x i 1 + ... + a q x nq + b ( Z n z ) + b n ( Z n z ) x n 1 + · · · + b q ( Z n...
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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.
 Fall '09
 XIAYingcun

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