STA 606: Theory of Statistical Inference I
Spring 2015
Contact Information:
Instructor: Solomon W. Harrar, Ph.D.
Office Hours: WF 2- 3 PM or by Appointment
Office: MDS 347
Tel: (859)257-6903
Email:solomon.harrar@uky.edu
Class Time and Place: MWF 1-1:50 PM, MDS 337
Catalog Description: Convergence concepts (Central Limit Theorem), Sampling from a Normal Distribution, Order
Statistics, Methods for finding point and interval estimates, Methods for finding hypothesis tests, Sufficiency principle,
Methods for evaluating point estimators (mean square error, unbiasedness, Carmer-Rao lower bound), Asymptotic of
point estimates and interval estimates and hypothesis testing procedures.
Course Objectives: In STA 623, we developed the probabilistic tools and language of mathematical statistics. The
course described probabilistic models for and properties of random variables, common probability distributions, and
random samples. In the present course, STA 606, the theoretical underpinnings of statistical inference procedures
are studied. In particular, the theory of estimation, confidence sets and hypothesis testing are investigated.
Learning Goals:
1. To understand how to derive estimators and their properties, such as distribution, variance, bias, MSE, and
consistency and other asymptotic properties.
2. To understand the theory behind confidence intervals and hypothesis tests.
3. To understand asymptotics for likelihood theory and apply it to estimation and hypothesis testing.
4. To gain an understanding of the theory behind normal-based inference for one and two sample problems.
5. To be able to use software to obtain numerical solutions to problems where analytical solutions are not possible
and to carry out simulations to evaluate inference procedures and approximations.
Course Content:
1. Order Statistics (5.4)
2. Convergence Concepts (5.5)
3. Sufficiency (6.2)
4. Point Estimation (7.2)
5. Hypothesis Testing (8.2)
6. Interval Estimation (9.2)
7. Unbiased Estimation and UMVUE (7.3)
8. Asymptotic Methods (10.2, 10.4, 10.5)
Prerequisite: STA 623.
Text:
1. G. Casella and R. L. Berger. Statistical Inference, 2nd ed., Duxbury, 2002. (Errata on the seventh printing:
http://www.stat.ufl.edu/archived/casella/class/errata7.pdf)
References (Available in the library):
1. A. M. Mood, F.A. Graybill and D.C. Boes. Introduction to the theory of statistics, 3rd ed. McGRAW-HILL,
1974.
2. V. K. Rohatgi and A. K. Md. Ehsanes Saleh. An Introduction to Probability and Statistics, 2nd ed., Wiley
2001.
Course Assessment: Your final graded on the course will be based on Homeworks (25%), 1 Mid Terms (each
30%) and Final Exam (45%). Grades will be assigned based on the following scale: 85-100 ~ A, 70-84 ~ B, 60-69
~ C, 50-59~D, 0-49 ~ E.
Homework: Homework will be assigned once a week. Some of the homework problems may be based on materials
that are discussed in the book but not directly treated in class. I encourage you to ask questions in class. However,
in the interest of time, we may not be able to entertain all your questions related to homework problems or otherwise.
I will be more than happy to assist you during office hours or by setting up an appointment. Homework assignments
must be done cleanly in an 81/2 X 11 size papers, must be stapled (if extends more than one sheet of paper) and
proofs and answers must be written in complete sentences. Homeworks must be done individually. You are allowed
to discuss problems with other students but the final write-up must be your own. Homeworks are due on Wednesdays
by 1PM.
Exams:
 There will be one midterm and one cumulative final exam.
 The midterm exam will tentatively occur on March 13th and the final exam will occur on Wednesday May 6th
from 1-3PM.
 The coverage of the midterm will be announced at a later time.
Make up: If you cannot make it to an in-class exam due to a reason for which you can produce acceptable
documentation, please let me know as soon as possible so that we can arrange for a make-up exam. There will be
no make-up for homeworks. In the event that you cannot turn-in homework due to documentable and acceptable
reasons, I will impute missing homework scores with the median of your scores on the other homeworks. It would be
to your advantage to turn in homeworks in advance in the case of planned absence.
Expectations:
1. I expect you to be respectful to me and other students.
2. I expect you to attend class regularly. However, attendance and class participation will only have the obvious
indirect bearing on your course grade. In any event, the student is responsible to get caught up with the
materials covered and homework assigned.
3. I expect you to keep a positive attitude throughout the semester. The course is being shaped to meet the
needs of as many students as possible. All master's candidates are required to pass a comprehensive
departmental written examination on the content of a few courses including STA 623 and 606. This
examination is normally administered in late May/early June. I will teach the course keeping students who will
take comprehensive exam in mind.
4. Some lectures may be much more technical than others. For some theorems we will do detailed proofs when
the proof is enlightening to see the broader scope of applicability of the result. On the contrary, for some
examples the algebraic details could be tedious in which case I will leave them for you to verify. I expect you
to fill in all the details on your own. I will be happy to assist you during office hours if you have difficulty
verifying them.
Website:
I
will
maintain
webpage
for
this
course
at
the
website
http://ashouston.ad.uky.edu/statistics/users/sha274/STA606/. On the web page, some relevant information pertaining to
schedule, homework assignments and R-codes from class will be posted. Also other course related announcements
will be posted. Please check the website regularly, at least three times a week (every class day).
Some Dates You May Want to Know:
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January 19 - Monday - Martin Luther King Birthday - Academic Holiday
January 21 - Wednesday - Last day to add a class for the 2015 Spring Semester
February 4 - Wednesday - Last day to drop a course without it appearing on the student’s transcript
February 4 - Wednesday - Last day to change grading option (pass/fail to letter grade or letter grade to
pass/fail; credit to audit or audit to credit)
March 16-21 - Monday through Saturday - Spring Vacation - Academic Holidays
May 1 - Friday - Last day of classes
Disability: If you have a documented disability that requires academic accommodations, please see me as soon as
possible during the scheduled office hours. In order to receive accommodations in this course, you must provide me
with a Letter of Accommodation from the Disability Resource Center (Room 2, Alumni Gym, 257-2754,
jkarnes@uky.edu) for coordination of campus disability services available to students. We can then work together to
find the best solutions for you.
Student Code: All students need to be familiar
http://www.uky.edu/StudentAffairs/Code/part1.html.
with
the
Student
Code
of
Conduct
found
at
Academic Integrity: All students must practice academic honesty. Academic misconduct is subject to an academic
penalty by the course instructor and/or a disciplinary sanction by the University.