STAT 652: Statistical Inference

Section 002

Instructor: Clifton D. Sutton

Text:

Prerequisite:

Description:

• provide a foundation for the advanced study of statistics (which should allow for a deeper undersanding of applied methods);
• provide background which should make the literature of statistics more accessible;
• and (perhaps most importantly) cover important general methods which can be applied to problems not typically addessed in books, and be used to obtain theoretically-based solutions.

• cover some somewhat advanced probability material (typically not given enough attention in 500-level probability courses);
• cover general statistical principles and "building block" statistical concepts;
• cover many common general methods for obtaining decent point estimates, confidence intervals, and tests of hypotheses, and learn how to apply them to obtain estimates and perform tests in a wide variety of parametric model situations.

Approximate week-by-week content:

[1] Jan. 22:

exponential families; location and scale families
[Sections 3.4 and 3.5 of text]
(HW #1 posted)

[2] Jan. 29:

random samples; sums of random variables; sampling from normal distributions, sample minimums and maximums
[parts of Sections 5.1, 5.2, 5.3, and 5.4 of text]

[3] Feb. 5:

convergence concepts
[Section 5.5 of text]

[4] Feb. 12:

more on convergence concepts, the sufficiency principle
[Section 5.5 of text, Section 6.2 of text]
(HW #1 due; HW #2 posted)

[5] Feb. 19:

more on the sufficiency principle, the likelihood principle; the equivariance principle
[parts of Sections 6.2, 6.3, and 6.4 of text]

[6] Feb. 26:

point estimation methods
[Section 7.2 of text (subsection 7.2.4 won't be covered)]
(HW #2 due; HW #3 posted)

[7] Mar. 4:

more on point estimation methods; evaluation of point estimators
[Sections 7.2 and 7.3 of text (subsection 7.2.4 won't be covered)]

[**] Mar. 11:

No class due to Spring Break

[**] Mar. 18:

No class due to extended Spring Break

[8] Mar. 25

more on the evaluation of point estimators, UMVUEs
[Section 7.3 of text]
(HW #3 due; HW #4 posted)

[9] Apr. 1:

Pitman estimators and Bayesian estimation
[Subsections 7.2.3 and 7.3.4]

[10] Apr. 8:

hypothesis testing
[Section 8.2 of text (subsection 8.2.2 won't be covered) and Section 8.3 of text]
(HW #4 due; HW #5 posted)

[11] Apr. 15:

likelihood ratio tests
[Subsection 8.2.1]

[12] Apr. 22 :

confidence intervals
[Section 9.2 of text]
(HW #5 due; HW #6 posted)

[13] Apr. 29:

more on confidence intervals; asymptotics pertaining to point estimation
[Section 9.2 of text (and a bit about Sec. 9.3); Section 10.1 of text (subsection 10.1.4 won't be covered)]
(remainder of HW #6 posted)

[14] May 6:

asymptotic methods for hypothesis testing and confidence intervals
[Sections 10.3 and 10.4 of text]
(HW #6 due (no grace period))

[**] May 13:

Take-home Final Exam due at 10:15 PM

Grading:

• 33.3% for homework assignments
• 66.7% for open book (and notes) take-home final exam

Additonal Comments:

• 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).
• All GMU students are expected to activate their GMU e-mail accounts and check them regularly for messages from the university administration and their instructors (although I tend to use the announcements web page of my course websites as my primary way of communicating with students).
• Be sure to note that there is not a class meeting scheduled for March 11 (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 Wednesday 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 Wednesdays I do not like to be bothered from 7:00 to 7:20 and on Mondays and Tuesdays I tend to be quite busy with my other classes (until somewhat late at night). My guess is that Thursday and Friday afternoons between 1:30 and 3:00 will generally work out best for meeting outside of office hour time (although during the first month of the semester I may often be busy with consulting center work during those times). I am willing to stay in the classroom and assist people each Wednesday after class.
• Please do not leave long messages on my voice-mail. But 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 typically have at least two weeks to complete each homework assignment, except that I may not cover all of the material pertinent to 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 Wednesday class meeting when it is due, typically you can turn it in to me up until noon the following Thursday. (I will post the due dates and the grace period information on the homework web page. For the assignment due at our last regular class meeting, there will be no grace period (since I plan to distribute the solutions in class that night).) To encourage you to not delay doing the homework, I may refuse to answer questions about an assignment after 10:30 PM on the Wednesday it is due. After the end of the grace period (typically noon on the Thursday following the nominal due date, 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 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. You can possibly fax your papers to me at (703) 993-1700. (If you do fax your paper, 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 boxes 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 generally discuss homework problems with others (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. (To clarify, you shouldn't give someone your homework solutions to look at, or explain to them in detail how you solved a problem. Discussion of homework problems should be kept at a rather general level, and sharing of specific details should be avoided.) If I believe that some students aren't respecting my policies about working too closely together I will give the class a warning, and if the problem persists I'll state that students can no longer have any discussions about how to solve homework problems and indicate that it'll be an Honer Code offense if you do so (and if this happens, I'll have an obligation to turn in students to the Honor Committee if I suspect their work does not reflect their own efforts and abilities, or if their solutions are unusually similar to those of another student).
• You are expected to submit your final exam solutions by 10:15 PM on May 13; 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).
• If you are a student with a disability and desire academic accommodations, please see me during the first two week of classes and contact the Office of Disability Services (ODS). All academic accommodations must be arranged through the ODS.
• Any class meetings canceled by the university due to snow, sleet, power outage, bombing, etc. will be made up if possible. 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).