midterm - STA 414S/2104S: TakeHome Midterm Test. Due March...

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STA 414S/2104S : TakeHome Midterm Test. Due March 25, 2010 before 2 pm. Please work alone. 1. (Adapted from Exercise 2.7, HTF). Suppose we have a sample ( y 1 ,x 1 ) ,..., ( y N ,x N ), and we assume the model y i = f ( x i ) + ± i , (1) where f ( · ) is an unkown regression function, ± i N (0 2 ), and the ± ’s are independent. A fairly wide class of estimators considered in the course are of the form ˆ f ( x 0 ) = N X i =1 i ( x 0 ; x ) y i , where x = ( x 1 ,...,x N ). (a) Show that linear regression and k -nearest neighbour regression are members of this class of estimators, and describe the weights i ( x 0 ; x ) in each of these cases. (b) STA 2104 only Decompose the conditional mean-squared error E y | x { ˆ f ( x 0 ) - f ( x 0 ) } 2 , where the expectation is over the conditional distribution of y 1 ,...,y N , given x 1 ,...,x N . 2. (Adapted from Exercise 2.1, R.A. Berk). Figure 1 shows a plot of Ozone against Temperature, from a database of daily measurements in New York over 154 summer days. The following fits are summarized in the code extract: > data(airquality);attach(airquality) > library(gam)
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midterm - STA 414S/2104S: TakeHome Midterm Test. Due March...

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