10.2. This problem continues using the infrared data on extragalactic objects and the variable X (the log of the 12-m-band flux measurement) from Problem 10.1.

10.2. This problem continues using the infrared data on extragalactic objects and the variable X (the log of the 12-μm-band flux measurement) from Problem 10.1. The dataset also includes F100 data: the total 100-μm-band flux measurements for each object. Denote the log of this variable by Y. Construct bivariate density estimates for the joint density of X and Y using the following approaches.

a. Use a standard bivariate normal kernel with bandwidth matrix hI2. Describe how you chose h.

b. Use a bivariate normal kernel with bandwidth matrixH chosen by Terrell’s maximal smoothing principle. Find a constant c for which the bandwidth matrix cH provides a superior density estimate.

c. Use a normal product kernel with the bandwidth for each coordinate chosen using the Sheather–Jones approach.

d. Use a nearest neighbor estimator (10.48) with a normal kernel. Describe how you chose k.

e. Use an Abramson adaptive estimator with the normal product kernel and bandwidths chosen in the same manner as Example 10.7.