STAT 5381 - Trindade

STAT 5381 -- Advanced Mathematical Statistics II -- Spring 2017

Basic Information

Course instructor: Dr. Alex Trindade, 228 Mathematics & Statistics Building.
E-mail: alex.trindade"at"ttu.edu; Phone: 834-6164.
Course Meets: MWF 12:00-12:50 in MATH 115.
Office Hours: Wed 3-5, Thurs 12-1, or by appointment.

Books & Notes

Gentle's Theory of Statistics notes.
Testing Statistical Hypotheses (TSH), by Lehmann and Romano, 3rd ed., 2005, Springer. (From TTU library as an e-book.)
Likelihood Methods in Statistics, by Severini, 2000, Oxford.
Theory of Statistics, by Schervish, 1995, Springer.
Mathematical Statistics, by Shao, 1999, Springer.

Course Objectives and Syllabus

STAT 5381 aims to provide a solid theoretical foundation for statistical inference (hypothesis tests and confidence sets). It employs a probabilistic and measure theoretic approach to formulate and solve statistical inference problems. Material to be covered: uniformly most powerful (UMP) tests; uniformly most powerful unbiased (UMPU) tests; optimality in the context of exponential families; uniformly must accurate (UMA) confidence sets; asymptotically optimal (AUMP) tests; Likelihood-based tests (likelihood ratio, Wald, Score); asymptotic distributions and higher-order approximations; Edgeworth expansions and saddlepoint approximations; inference in the presence of nuisance parameters based on conditional, modified, and integrated, likelihoods; the modified profile likelihood. This coverage corresponds to the following core topics:

UMP Tests (TSH: ch. 3)
UMPU Tests (TSH: chs. 4 & 5)
AUMP Tests (TSH: chs. 11-13)
Likelihood-based Tests (Severini: ch. 3-4)
Higher-order asymptotic approximations (Severini: chs. 5 & 6)
Inference in the presence of nuisance parameters (Severini: chs. 7-9)

Expected Student Learning Outcomes

Students will learn the theory behind optimal statistical hypothesis tests and confidence set construction, and will be capable of providing a solid theoretical justification and understanding for common statistical methods used in practice. Students can expect to spend several hours per week outside of instructional time on reading, homework, and exam preparation.

Methods of Assessing the Expected Learning Outcomes

The expected learning outcomes for the course will be assessed through: homework sets, semester tests, and a final exam. The course grade will be determined from homework problem sets (20%), two semester tests (25% each), and a comprehensive final exam (30%). The traditional grading scale will be used:

A: 90-100%.
B: 80-89%.
C: 70-79%.
D: 60-69%.
F: 0-59%.

Homework Problem Sets

There will be weekly problem sets due on thursdays. You are expected to do all the assigned problems, but only a subset may actually be graded. Start each problem on a separate page. All work handed in must be stapled together. No late submissions will be accepted.

Policies

Class Attendance. Your attendance alone will not impact your grade, but missing exams and assignments will. Whether an absence is excused or unexcused is determined solely by me, with the exception of absences due to religious observance and officially approved trips (see below).
- Make-up Exams: These may be granted in exceptional circumstances if you provide me with a valid excuse (such as a note from a physician, an obituary, etc.).
- Absence due to religious observance: The Texas Tech University Catalog states that a student shall be excused from attending classes or other required activities, including examinations, for the observance of a religious holy day, including travel for that purpose. A student who intends to observe a religious holy day should make that intention known in writing to the instructor prior to the absence. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence.
- Absence due to officially approved trips: The Texas Tech University Catalog states that the department chairpersons, directors, or others responsible for a student representing the university on officially approved trips should notify the student's instructors of the departure and return schedules in advance of the trip. The instructor so notified must not penalize the student, although the student is responsible for material missed. Students absent because of university business must be given the same privileges as other students.
Illness and Death Notification. The Center for Campus Life is responsible for notifying the campus community of student illnesses, immediate family deaths and/or student death. Generally, in cases of student illness or immediate family deaths, the notification to the appropriate campus community members occur when a student is absent from class for four (4) consecutive days with appropriate verification. It is always the student's responsibility for missed class assignments and/or course work during their absence. The student is encouraged to contact the faculty member immediately regarding the absences and to provide verification afterwards. The notification from the Center for Campus Life does not excuse a student from class, assignments, and/or any other course requirements. The notification is provided as a courtesy.
Students with Disabilities. Any student who because of a disability may require special arrangements in order to meet course requirements should contact the instructor as soon as possible to make any necessary accommodations. Student should present appropriate verification from AccessTECH. No requirement exists that accommodations be made prior to completion of this approved university procedure.
Civility in the Classroom. It is expected that everyone will behave in a manner that is conducive to learning. One common disruption is cell phones. Please turn these off in class.
Academic Integrity. Is assumed and expected at all times. Students are advised to acquaint themselves with the Code of Student Conduct.
It is the aim of the faculty of Texas Tech University to foster a spirit of complete honesty and a high standard of integrity. The attempt of students to present as their own any work that they have not honestly performed is regarded by the faculty and administration as a serious offense and renders the offenders liable to serious consequences, possibly suspension.
Collaboration. My specific policies are as follows.
- Homeworks: Discussion with peers regarding material/concepts covered in the course is permitted, and is encouraged since it usually leads to greater comprehension. However, each person must write up his/her own solution to a particular problem, and not simply copy it from someone else.
- Tests: Any form of collaboration in tests, including trying to see what the person next to you is writing, is strictly forbidden and will not be tolerated.

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