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 3 by setting m = 128. The thresholded wavelet estimate requires a dyadic number n of points xi, say n = 2J 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 Friedman'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 3
Reduce the size of the sunspots data from Problem 2 by taking only the first m observations:
At what value of m does the cross-validation method begin to provide a reasonable estimate? Why is this occurring?