STAT 652 / CSI 672: Statistical Inference

Instructor: Clifton D. Sutton

Texts:

• Statistical Inference, 2nd Ed. , by G. Casella & R. L. Berger (Duxbury, 2002)
• Introduction to Probability and Mathematical Statistics, 2nd Ed., by L. Bain & M. Englehardt (Duxbury, 1992)

Prerequisite:

Description:

Approximate week-by-week content:

[1] Jan. 24:

introduction; limiting distributions (convergence in distribution)

[2] Jan. 31:

stochastic convergence (convergence in probability) and more advanced probability concepts (Slutsky's theorem, the mgf approach to limiting distributions, the central limit theorem)

[3] Feb. 7:

introduction to statistical models; sufficient statistics

[4] Feb. 14:

exponential families; some basic properties for point estimators; point estimation methods (frequency substitution, the method of moments, maximum likelihood estimates)

[5] Feb. 21:

more on methods of estimation (more on maximum likelihood estimation, least squares estimates, the minimum distance method, minimum chi-square estimates)

[6] Feb. 28:

point estimation as a statistical decision problem and optimality (loss functions, risk, and admissibility); minimax estimates and Bayes estimates

[7] March 7:

more on Bayesian estimation, the Rao-Blackwell theorem, the Lehmann-Scheffé theorem, and UMVUE's

[**] March 14:

(No class due to Spring Break, but I may decide to hold a special office hours session in the classroom from 7:20 to 10:00 PM on either Monday (3/13) or Tuesday (3/14) of Spring Break week to answer questions and to work HW problems from previous semesters if people ask to see more examples)

[8] March 21:

the information inequality (the Cramér-Rao lower bound)

[9] March 28:

invariant estimation; additional criteria for comparing estimators (Pitman-closer estimators, more-concentrated estimators)

[10] April 4:

large sample theory (asymptotics) for point estimation

[11] April 11:

confidence intervals (pivotal quantities, properties of interval estimators)

[12] April 18:

more on confidence intervals (large sample results, an additional exact technique, confidence regions of higher dimension)

[13] April 25:

an introduction to hypothesis testing; optimal tests of statistical hypotheses (the Neyman-Pearson lemma, monotone likelihood ratio families)

[14] May 2:

generalized likelihood ratio tests; large sample approximations in testing

[**] May 9:

Final Exam (note: exam period is from 7:30 to 10:15 PM)

Grading:

• 50% for homework assignments (there will be about 115 points worth of HW assigned throughout the semester, but I'll truncate your point total at 100, thus allowing you to skip or miss some of the assigned homework without penalty)
• 50% for open book (and notes) final exam

Additonal Comments:

• It is necessary that each student buy a set of lecture notes from the bookstore (but I'll supply you with notes to cover the first two weeks of the semester). These notes are considered to be required in that I will feel free to refer to them often and so I expect that you will want to have them with you during each class meeting. (The notes may not be available in the bookstore until the second week of classes (but again, I will give you notes in class to cover the first two lectures).)
• Put STAT 652 in the subject line when you send me e-mail (due to spam, I sometimes delete messages without reading them, based on the subject line).
• Be sure to note that there is not a class meeting scheduled for March 14 (due to Spring Break). However, if any class meetings are canceled prior to Spring Break (perhaps due to bad weather), it could be that the Monday or Tuesday of Spring Break will be used to make up for the missed class.
• I can possibly make arrangements to meet with you outside of my scheduled hours; however, on Tuesdays I do not like to be bothered from 7:00 to 7:17 and on Mondays and Fridays I'm tied up with other activities for most of the day. I am willing to stay in the classroom and assist people each Tuesday after class. When my spring semester routine gets a little more settled, I may post additional information about my availability here.
• Please do not leave long messages on my voice-mail, and since I often don't get around to returning calls until the evening, you should state what time you plan to go to sleep. Always leave your phone number, speaking slowly, even though you might have given it to me previously. I find it better to communicate with people in person or via e-mail --- phone tag is frustrating and sometimes the GMU voice-mail system doesn't work the way it is supposed to.
• You will have at least two weeks to complete each homework assignment, except that I may not give you part of the final assignment until one week prior to its due date. If for some reason you don't have your paper ready to turn in the at the Tuesday class meeting when it is due, you can turn it in to me up until 9:00 PM the following Thursday (except for the last assignment, which must be turned in on the Tuesday it is due). But I encourage you not to get into the habit of treating Thursday as the due date since in that case you may feel that the work is crammed together too much at the end of the semester. To encourage you to not delay doing the homework, I may refuse to answer questions about an assignment after 10:30 PM on the Tuesday it is due. After 9:00 PM on the Thursday following the nominal due date (again, except for the last assignment which cannot be submitted late), late papers will be considered only if I haven't already graded the papers of other class members. (I really mean this! And 4 feet of snow or a broken fax machine does not change things --- if I don't have your paper by the end of the grace period, I won't grade it if I've already graded the other papers. If you plan to fax your paper, you should perhaps plan to do it by Wednesday, and not wait until Thursday.) If you bring your paper by my office and I'm not there, the best procedure is to put it under my office door and then send me an e-mail or call and tell me that you dropped off your paper. (If you come by to drop your paper off outside of usual business hours, and find that the doors to my building (the Central Module) are locked, it should be okay to put your paper under the glass door of my department's main office, which is located in Science-Technology 2 (room 158).) You can possibly fax your papers to me at (703) 993-1700. If you do make use of the fax, please notify me by e-mail or phone so that I can look for your paper. (The entire department shares the same fax machine.) I cannot be responsible for late papers put under my door or faxed if for some reason I don't get them, but in the past I've never had too many problems getting papers in these ways (although the new fax machine seems to not work as well as the old fax machine did). Do not e-mail solutions to me.
• All homework should be on paper which is approximately 8.5 inches by 11 inches. All pages should be stapled in the upper left hand corner. All answers should be clearly indicated. (You need to choose one answer for each part. Draw a box around your final answers or highlight them in some way.) You should show adequate supporting work and not merely give answers.
• You are expected to familiarize yourself with the George Mason University honor code and abide by it. It is perfectly okay to seek assistance from others on any of the homework problems (except for extra credit problems, which may be occassionally assigned), but you should not turn in any work that is copied from someone else (and so you should be prepared to explain your solution to me if asked to do so). It will be considered to be a violation of the honor code if you deviate from this rule concerning homework or if you give or receive aid on the final exam.
• You are expected to take the final exam during the designated time slot; Incompletes will not be granted except under very unusual circumstances.
• Please abide by the university policy that cell phone ringers be turned off while class is in session.
• Please do not make a lot of noise eating during class --- if you feel that you must eat during class, please choose a soft candy bar rather than a bag of potato chips (since both the chips and the bag they come in tend to make too much noise when eaten and handled).
• Any class meetings canceled by the university due to snow, sleet, power outage, bombing, etc. will be made up if possible (at a time to be agreed upon by me and as many members of the class as is possible if the univeristy doesn't specify a particular make-up date). With regard to bad weather, I will plan to teach class if the university is open and not teach it if the university is closed. So instead of calling me to find out if I plan to have class, just find out if the university is open or closed.
• Caveat: The schedule and procedures described here for this course are subject to change (and it is the responsibility of students to attend all class meetings and keep themselves informed of any changes).