(a) Use splitting the data to choose the side lengths of rectangular partitioning such that the resulting estimate approaches the rate of convergence in Problem 4.7. (b) Use splitting the data to...

(a) Use splitting the data to choose the side lengths of rectangular partitioning such that the resulting estimate approaches the rate of convergence in Problem 4.7.

(b) Use splitting the data to choose the scaling for product kernel estimates such that the resulting estimate approaches the rate of convergence in Problem 5.7.

(c) Our results in Chapter 6 concerning nearest neighbor estimates used the Euclidean distance. Obviously, all the results of this chapter hold with scaling, i.e., for norms defined by

                          x2 = d j=1 cj |x(j) | 2 ,

 where c1,...,cd > 0 are the scaling factors. Use splitting the data to choose the scaling factors together with k for k-NN estimates based on such norms.