Eric
 
Attached are the handouts I used yesterday. The one directly based on your notes had
a couple of typos, which I have now fixed. Also made a few nonsubstantive changes in
wording. Some students were asking if these would be posted. Suggest posting PDFs,
but I'm sending MS Word versions also, in case you want to modify these for the future.
 
Ideas stressed
 
1) To work irreg MLE problems, you have to take the condition that specifies the support
of the joint density of the sample (which is framed in terms of conditions on data for given
parameters) and turn that condition into one that is more friendly to viewing the joint
density as a likelihood function (which needs to be framed in terms of conditions on the
parameter given the data.
 
2) Although irregular MLEs need not be asymptotically normal, unbiased versions of them
still have smaller variances than do other unbiased estimators. This was discussed mainly
in terms of RESULTS of the R code. I spent almost no time with details of the R code.
Said it was a quick way of avoiding the analysis, some of it easy, some harder, to
find means, variances, and (for biased estimators) MSEs. I told them that
MSE = Var + bias-squared, so MSE = Var for unbiased estimators. Also told them
that quantiles are asymp normal, except for max and min. (In giving simulation results
it is best to show SDs and sqrt of MSE to keep everything in terms of the origl data
units.)
 
The 2nd handout on estimation of theta in samples from UNIF(0, theta) was covered only
briefly to look at the pictures. There is some analysis in there--skipped entirely. Told them
they should consolidate what I had shown them about irreg MLEs by showing that
the max is the MLE of theta in this case. (But not a formal assignment to turn in.)
 
Spent about 1/2 hr on tips for studying for MS Exam and strategies for taking it.
 
BT
 


-- 
B. E. Trumbo
Department of Statistics and Biostatistics
California State University, East Bay (Hayward)
Professor Emeritus of Statistics and Mathematics
Graduate coordinator