Problems: Assignment 6

- Page 365. Q 21.
- Page 365 Q 24.
- Page 366. Q 28.
- Page 366. Q 29.
- Suppose are iid and
are iid .
- Find complete and sufficient statistics.
- Find UMVUE's of and .
- Now suppose you know that . Find UMVUE's of
and of . (You have already found
the UMVUE for .)
- Now suppose and are unknown but that you
know that . Prove there is no UMVUE for .
(Hint: Find the UMVUE if you knew with
**a**known. Use the fact that the solution depends on**a**to finish the proof.) - Why doesn't the Lehmann-Scheffé theorem apply?

- Find complete and sufficient statistics.
- Suppose iid Poisson( ). Find the
UMVUE for and for .
- Let be the error sum of squares in the
**i**th cell in the question 5 of Assignment 5.- Find the joint density of the .
- Find the best estimate of of the form in the sense of mean squared error.
- Do the same under the condition that the estimator must be unbiased.
- If only are observed what is the MLE of ?
- Find the UMVUE of for the usual one-way layout model,
that is, the model of the last two questions.

- Find the joint density of the .
- Exponential families: Suppose are iid with density
- Find minimal sufficient statistics.
- If are the minimal sufficient statistics show
that setting and solving gives the
likelihood equations. (Note the connection to the method of moments.)

- Find minimal sufficient statistics.

Sun Oct 27 19:00:53 PST 1996