Stat 426 Estimation and Sampling Theory Winter 2008

Instructor: Allan Rossman
Class Times: MTWR 8:10-9:00, room 14-250
Office: Faculty Office Building East 25-102
Phone: 756-2861 (6-2861 on campus)
Email: arossman@calpoly.edu
Office Hours: MWF 10:10-11:00am in 25-102, TuTh 3:10-4:00pm in 02-206, and by appointment and by chance
Text: Probability and Statistics (3rd edition), by Morris H. DeGroot and Mark J. Schervish

Course Webpage: http://statweb.calpoly.edu/arossman/stat426/

Overview: This course provides a link between probability theory and the foundations of statistical inference, focusing on the important concept of estimation. We will begin by considering the concept of expectation, and then we will study special classes of probability distributions. Then we will shift from probability to statistics, studying techniques of estimation (such as Bayesian and maximum likelihood) and also properties of estimators (such as unbiasedness and sufficiency). An important idea throughout will be sampling distributions of estimators. We will follow the text fairly closely, but I will also introduce some additional material.

Goals: By the conclusion of the course, I hope that you have improved your ability to:

• understand concepts of estimation and sampling
• derive and prove results in probability and statistics
• apply probability and statistical methods to solve problems
• use the computer to investigate statistical phenomena
• communicate your knowledge of statistical ideas effectively

Class Policies: I expect class meetings to be fairly informal. During most class meetings I will present new material, but at times I may ask you to work on problems or activities. I strongly encourage you to bring questions to class and to ask questions as they occur to you.

Please come prepared to participate in class. By this I primarily mean two things:

• Please read relevant sections of the text before coming to class. Read carefully, and come to class with questions on what you do not understand.
• Please be willing (or, even better, eager!) to ask questions and contribute answers and work on problems (when I ask you to) during class.

I also expect you to devote 8-12 hours per week, outside of class time, to your work for this course. I anticipate that this work will be divided among:

• reading the textbook
• reviewing your class notes
• working on assignments

Grading Policies: Your course grade will be determined by the following components, with relative weights as indicated:

• assignments (25%)
• two midterm exams (45%: 20% for your lower score, 25% for your higher score)
• final exam (30%)

Assignments: Homework assignments will be made roughly weekly. You are encouraged to discuss homework problems with each other, but your solutions must be written up individually in your own words. I urge you to ask questions about these problems (ahead of time!) inside and outside of class. Some of the homework problems will be taken from the text. Be aware that answers to many odd-numbered questions appear in the back of the book, but of course you will be graded on your method of solution and clarity of explanation. Some of the problems will also involve computing; you will given instructions for using Minitab, but you are welcome to use SAS or S-plus or R or another package. For these problems, integrate relevant computer output into your write-up.

All assignments are due at 4pm on the indicated day. You may have a 24-hour extension on the due date for one of the assignments; other than that, late assignments will not be accepted except for very compelling circumstances.

The purposes of these assignments are:

• to give you the practice with proof and problem-solving techniques in order to learn, understand, and apply the course material,
• to provide you with feedback regarding your understanding of the material,
• to further your discovery and exploration of course material,
• to improve your abilities to communicate well and to use computing, and
• to prepare you for the kinds of questions that will be on the exams.

Exams: You will received detailed guidelines regarding the exams a week or so in advance. They will be open-book and open-notes, and they will involve both in-class and take-home components. The final exam will focus on more recent material but will also have a cumulative component. You may make up an exam only with a written medical excuse.

Advice: With apologies to David Letterman, I offer the following “Top Ten” suggestions to improve your learning in this course:

• Come to class.
• Participate in class.
• Invest time outside of class.
• Read the text.
• Ask questions.
• Use office hours.
• Study together.
• Start the assignments early.
• Take pride in your work.
• Think!

A common theme emerges from this list: You are responsible for your own learning. As your instructor, I view my role as providing you with contexts and opportunities that facilitate the learning process. Please call on me to help you with this learning in whatever ways I can.

Tentative Schedule: The following is always subject to change but should give you a sense for what topics we will cover and when:

Week	Dates	Topics	Sections from Text
1	January 7-10	Covariance, Correlation, Conditional Expectation	4.6, 4.7
2	January 14-17	Sample Mean, Law of Large Numbers, Discrete Distributions	4.8, 5.1, 5.2, 5.3, 5.4, 5.5
3	January 22-24	Normal Distribution, Central Limit Theorem, Other Continuous Distributions	5.6, 5.7, 5.8, 5.9, 5.10
4	January 29-February 1	Multinomial, Multivariate Normal Distributions, Exam	5.11, 5.12
5	February 5-8	Prior and Posterior Distributions, Conjugate Priors	6.1, 6.2, 6.3
6	February 12-15	Bayes Estimators, Maximum Likelihood Estimators	6.4, 6.5, 6.6
7	February 19-22	Method of Moments, Unbiased Estimators	7.7
8	February 26-29	Mean Squared Error, Exam
9	March 4-7	Chi-Square and t- Distributions, Joint Distribution of Sample Mean and Variance	7.1, 7.2, 7.3, 7.4
10	March 11-14	Confidence Intervals, Hypothesis Tests	7.5, 8.1
	Friday, March 21	Final Exam (7:10-10:00am)

Disclaimer: I am not always as organized as this lengthy syllabus might suggest. All of these details are subject to change as the course develops. I welcome and value your input.