Ex. 6.10 Suppose we have N samples generated from the model 3;, = f(.r,;) + 13., with a, independent and identically distributed with mean zero and variance 02, the I1: assumed xed (non random). We estimate 3" using a linear smoother (local regression, smoothing spline, etc.) with smoothing parameter A. Thus the vector of tted values is given by i' = S H'- Consider the inusomple prediction error 1 N 2 E3212": . m 3%)) (6.34) for predicting new responses at the N input values. Show that the aver; age squared residual on the training data, ASRQ), is a biased estimate (optimistic) for PEQ}, while o, = asap} + 2%tracgsg (5.35) is unbiased