Explanation of answers to Quiz #11
Everyone who took the quiz got the 1st two parts
correct, but only two got the last one right. (This leads me to believe
that I needed to express that part better, but rather than make an
adjustment to the scores, I'll just let them stand as is (with an answer
of true counted as being incorrect) since pretty much everyone is
in the same boat. But I'll partially make it up to you by indicating
here that one of the final exam questions will deal with the proper bin
width for a histogram density estimate.)
(I've reconsidered, and decided not to count
true as being wrong. I didn't word the question well enough to
make sure I should get the answer I was looking for. Still, you can read below
for more information about what I had in mind. Also, I'll still make
one of the small final exam questions about the proper bin width
for a histogram estimator.)
I was hoping that the statement on p. H13 of the class notes that
suggests that in cases for which there is no general agreement from
indications of the proper value for h that one should choose a
density estimate that "exhibits a small amount of local noise" would
lead you to answer false. (An estimate which is good using ISE as
a measure of goodness is typically bumpier than the true underlying
density. A larger than optimal bin width is often needed to make an
estimate of a unimodal density have only one mode, but the wider bins
hurt the overall quality of the estimate. In many cases, a good
histogram estimate can leave one uncertain about the number of
modes that the estimand has. One strategy is to ignore the "local
noise" since such noise is to be expected, but by doing this there is often a
sizable risk of not correctly identifying the modes of a multimodal density.)