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Unformatted text preview: Tutorial 9 1. Suppose we need to estimate a varying coeﬃcient model Y = a0 (x1 ) + a1 (x2 )x3 + ε with sample (xi1 , ..., xi3 , Yi ), i = 1, ..., n. Using cubic spline to approximate ak (z ). (a) write the expression for the estimator of a1 (z ) (b) ﬁnd the 95% conﬁdence band for a1 (x). 2. Suppose we have ((data set), using one knot t1 = 0.5 for both x1 and x2 , ﬁt the above model in question 1. 3. Suppose we have data (xi , yi ), i = 1, ..., n and need to estimate g (x) = E (yi |xi = x). ˆ Let Y = (y1 , ..., yn ) and the ﬁtted value of Y be Y. Show that both kernel smoothing (NW estimator and local linear kernel estimator) and polynomial splines methods have the following form ˆ Y = S Y. give the details for S for diﬀerent methods. 4. For the baseball player’s salary data ((data set). (a) ﬁnd suitable transforms to the variables (such that its histogram looks symmetric). (b) Compare the follows methods for prediction of y based on CV. (1) Generalized additive model, (2) PPR with 2 components, (3) CART and (4) MARS. 1 ...
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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