I'm groping for some compelling graphical presentation of Expectation,
within an exponential family with a single real parameter would be more
than enough.
If, for example, I create a contour plot of Likelihood, given a real
sufficient statistic and a real parameter, then I can give a reasonably
compelling argument showing how the maximum likelihood estimator of the
parameter follows from the sufficient statistic, how these two relate.
What I would like to find is some analogous meaningful function of that
parameter and statistic, perhaps such that maximizing that function would
give a reasonably compelling argument showing how the expected value of
the sufficient statistic follows from the parameter.
I understand I can integrate x*f(x) over the domain and that this is the
definition of expectation. All that is clear and understood. I know that.
What I'm groping for would be some graphical presentation that I could do
that would be similar to the graphical presentation for MLE.
I have tried to do my homework. I've looked through some of the journals.
I paged through "Statistical Methods: The Geometric Approach" by Saville
and Wood, thinking they might have given some graphical presentation of
expectation, but I didn't find it.
I realize I can craft up A function whose maxima accomplishes this. But
I've not been able to see a meaningful function underlying this. And I
thought that such a function might even give additional insight into
expectation somehow.
Can anyone offer some ideas?
Thank you
Don
-----= Posted via Newsfeeds.Com, Uncensored Usenet News =-----
http://www.newsfeeds.com - The #1 Newsgroup Service in the World!
-----== Over 80,000 Newsgroups - 16 Different Servers! =-----
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
