Using the first m = 128 observations from the sunspots data in Problem 2, obtain the wavelet estimate using the VisuShrink method from Chapter 13. Comment on the graphical comparison between the VisuShrink estimate and the estimate you would have gotten in Problem 11 by setting m = 128. The thresholded wavelet estimate requires a dyadic number n of points x_i, say n = 2^J for some integer J . Additionally, it assumes that these points are equally spaced apart. These two conditions are met by the truncated sunspots data. However, VisuShrink is designed for normal errors ε, while Clevelands's estimator makes no such assumption.

Problem 2

Consider the data set sunspots from Andrews and Herzberg (1985) as a response variable. For the predictor data x, use

Apply Friedman's smoother using trial and error to find a span that seems to work well with the data. Then find an estimate using the span determined by cross-validation. Describe the results (taking into account Comment 5).

Problem 11

Reduce the size of the sunspots data set by taking only the first m observations as was done in Problem 3. At what value of m do the cross-validation methods begin to provide reasonable estimates? Why is this occurring?

Problem 3

Reduce the size of the sunspots data from Problem 2 by taking only the first m observations: