. This problem continues using the infrared data on extragalactic objects and the variable X (the log of the 12- μ m-band flux measurement) from Problem 10.1. The dataset also includes F100 data: the...

.
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
h
I2. Describe how you chose
h.

b.
Use a bivariate normal kernel with bandwidth matrixHchosen byTerrell’s maximal smoothing principle. Find a constant
c
for which the bandwidth matrix
c
Hprovides 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.