Consider the bone mineral density data of Figure 5.6
(a) Fit a cubic smooth spline to the relative change in spinal BMD, as a function of age. Use cross-validation to estimate the optimal amount of smoothing. Construct pointwise 90% confidence bands for the underlying function.
(b) Compute the posterior mean and covariance for the true function via (8.28), and compare the posterior bands to those obtained in (a).
(c) Compute 100 bootstrap replicates of the fitted curves, as in the bottom left panel of Figure 8.2. Compare the results to those obtained in (a) and (b).
