MATH 667
Statistical Inference
Fall
Syllabus
Instructor:
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Textbook: Statistical Inference by George Casella and Roger L. Berger, second edition,
Duxbury, 2001
Additional Possible Textbooks:
• Mathematical Statistics. Basic Ideas and Selected Topics by Peter J. Bickel and Kjell A.
Doksum, second edition, Pearson, 2006
• Mathematical Statistics by Jun Shao, second edition, Springer, 2003
Prerequisites: MATH 561 or consent of department
Credit Hours: 3
Objective: This course covers advanced topics in mathematical statistics such as sampling
distributions, exponential families, sufficiency, point and interval estimation, likelihood-based
inference, hypothesis testing, Bayesian inference, statistical decision theory, and asymptotic
theory.
Learning Outcomes: Students who complete this course will understand important definitions
and be able to give rigorous proofs for important theorems covered in the course topics.
Furthermore, students will be able to use critical thinking skills by applying these definitions and
theorems to extend the results they have been taught and to apply the inference procedures to
related models and real data. Learning outcomes will be assessed through exams and homework.
Grade: One midterm, one final (150 points each), Homework (100 points)
392-400 A+, 372-391 A, 360-371 A348-359 B+, 332-347 B, 320-331 B308-3 19 C+, 292-307 C, 280-291 C268-279 D+, 252-267 D, 240-251 D
Others F
Tentative Schedule:
Chapter
week
1
3.4, 3.5
2
4.1, 4.2, 4.3
3
4.4-5.4
4
5
6
7
8
9
10
11
12
13
14
15
16
5.5, 5.6
6.1-6.2.3
6.2.3, 6.2.4
6.3, 7.2.2
7.2.3
7.2.4-7.3.3
7.3.4
8.1
8.2, 8.3
10.1
10.2
10.3
Contents
Exponential, Location, Scale Families
Multiple Random Variables
Properties of a Random Sample
Properties of a Random Sample
The Sufficiency Principle
The Sufficiency Principle
The Likelihood Principle
Point Estimation
Point Estimation
Point Estimation
Hypothesis Testing
Hypothesis Testing
Asymptotic Evaluations
Asymptotic Evaluations
Asymptotic Evaluations
Final Exam
Make-up work: Make-up exams will be given only in the case of a pre-arranged medical
procedure, university sanctioned event, or documented emergency. If you know in advance you
must miss an exam please let me know right away. In case of an emergency, please make every
reasonable effort to notify me within one day. Exams may not be taken early. All make-ups must
be scheduled through University Testing Services (852-6606). Missed quizzes cannot be made
up.
Incompletes: A grade of I may be given only if you have satisfied the conditions for an
incomplete as required by the College of Arts & Sciences:
• The majority of the course work must be completed by the end of the semester;
AND
• The performance in course work completed by the end of the semester must meet the published
standards for a passing grade;
AND
• The final portion of the course work could not be completed for reasons beyond the student’s
control.
In the event of an incomplete, the final exam must be completed prior to the dates listed at
jp://louisvil
to prevent an automatic change of grade from Ito F.
Academic Dishonesty: Academic dishonesty is prohibited at the University of Louisville. It is
a serious offense because it diminishes the quality of scholarship, makes accurate evaluation of
student progress impossible, and defrauds those in society who must ultimately depend upon the
knowledge and integrity of the institution and its students and faculty.
‘C
Students with Disabilities: The University of Louisville is committed to providing access to
programs and services for qualified students with disabilities. If you are a student with a disability
and require accommodation to participate and complete requirements for this class, notify me
immediately and contact the Disability Resource Center (Robbins Hall, 852-6938) for verification
of eligibility and determination of specific accommodations.
Religious Holy Days and Observances: Students who observe work-restricted religious holy
days must be allowed to do so without jeopardizing their academic standing in any course.
Faculty are obliged to accommodate students’ request(s) for adjustments in course work on the
grounds of religious observance, provided that the student(s) make such request(s) in writing
during the first two (2) weeks of term.
Attendance: Students are strongly encouraged to attend all lectures.
Standard Disclaimer: All content in this syllabus is subject to change. Occasionally
circumstances outside anyone’s control (earthquakes, windstorms, ice storms, floods, etc.) will
necessitate class cancellations and changes to the syllabus. Any revisions to the syllabus will be
announced in class and all changes will be posted on Blackboard.