The University of British Columbia - Vancouver
Statistics 305
Introduction to Statistical Inference
Term 2 of 2006 - 2007
BASIC COURSE INFORMATION:
Review of probability theory. Sampling distribution theory, large sample theory and methods of estimation and hypothesis testing, including maximum likelihood estimation, likelihood ratio testing and confidence interval construction.
STAT 200 (or BIOL 300) and MATH/STAT 302, or 65% in MATH/STAT 302.
STAT 200 is recommended.
3rd and 4th year students majoring in any of the mathematical sciences, and advanced undergraduate and graduate students from other disciplines seeking an exposition of the basic elements of the techniques of statistical inference.
The other main change is that many problems have been added in the 3rd edition, so be aware that the problem numbers in the 2nd and 3rd editions are different. If you plan on relying on a copy of the 2nd edition, it is your responsibility to sort this out as necessary!
Registration in each lab is capped due to room capacity, so one of the labs may be fully booked at the beginning of January. If you want to register in a lab that is currently full, just keep trying -- students will be switching labs, dropping the course and so on for the first while, so its a matter of timing.
Labs involving computational work will meet in Room 1 of the Mathematics and Statistics Resource Center (MSRC, 6357 Agricultural Road).
Labs involving no computational work will meet in MATH 204.
The labs are scheduled to begin the week of January 15-19. They will meet in MSRC that week.
ANNOUNCEMENTS:
EXERCISES:
You will want to work out lots of problems to master the course material. The textbook has many excellent problems, some worked out in detail in the chapters but many more at the end of each chapter.
If you are unsure of your mastery of material from MATH/STAT 302, for example, you should work through the material in Chapters 1-5 of the textbook and try to work out as many of the problems from those chapters as possible. Start with the odd-numbered problems as answers for some of these are given in the back of the textbook. Always work through the problem before looking at the answer provided -- you will learn much more than if you try to work backwards from the answer.
First try to work out the problems on your own, as you will gain much more confidence if you are able to do so. If you have trouble, ask some of the other students and try to solve the problem together. If you are still unsure of the solution (or even just the best approach to solving the problem), ask Reza (your TA) -- either in the labs or in the TA office hours -- or ask me immediately after class or in my office hours.
For # 16., do (a) and (b) and replace (c) and (d) with:
(c) Use the delta method to find a second-order approximation to
the expected value of the MME. What is the resulting expression for the
bias of the MME?
(d) Evaluate the (exact) bias of the MLE.
(e) Use the delta method to find an approximate expression for the
variance the MME.
(f) Evaluate an exact expression for the variance of the MLE.
(g) Use these results to evaluate the leading term in the mean
square error for both the MME and the MLE (the leading term will be of
order 1/n in both cases).
(h) Which of these two estimators would you prefer? Why?
Solution to 8.16
For # 50., do (a), (b) and (c) and add:
(d) Find the variance of the MM estimator (exact, not asymptotic).
(e) Compare the variances of the MM and ML estimators. Which
of these estimators would you prefer to use in practice? Why?
Solution to 8.50
MISCELLANEOUS MATERIAL:
OLD QUIZZES, MIDTERMS AND FINALS:
NOTE: Although the basic material covered in this course has not changed for several years, previous instructors may have presented the material in slightly different order and may have placed greater emphasis on slightly different aspects. So, the relevance of midterms from previous versions of the course is not entirely clear but they do provide additional "practice problems".
LABS:
Last updated: April 18, 2007