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DMtutorial8 - Tutorial 9 1 Suppose we need to estimate a...

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Tutorial 9 1. Suppose we need to estimate a varying coefficient model Y = a 0 ( 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 ). 2. Suppose we have ( (data set) , using one knot t 1 = 0 . 5 for both x 1 and x 2 , fit the above model in question 1. 3. Suppose we have data ( x i , y i ) , i = 1 , ..., n and need to estimate g ( x ) = E ( y i | x i = x ). Let Y = ( y 1 , ..., y n ) and the fitted value of Y be ˆ Y . Show that both kernel smoothing (NW estimator and local linear kernel estimator) and polynomial splines methods have
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