Statistics 630 – Overview of Mathematical Statistics

Sections 700 & 720, Spring 2010, Prof. D. Cline

Welcome!  This page announces and describes my course for the Spring 2010 semester.  (Further updates forthcoming.)

This course is intended for graduate students in various fields who require an introduction to mathematical statistics.  It covers basic probability theory, including random variables and their distributions, and the theory of statistical inference from the likelihood point of view, including likelihood estimation, confidence intervals, likelihood ratio tests and Bayesian methods.

The course will be taught online using lectures and notes prepared by Dr. Thomas Wehrly.  A weekly online question and answer session will be conducted by Dr. Daren Cline.

The R statistical programming software will be used throughout the course.

Course lectures, homework assignments, etc. will be posted at the DoStat website, but you will turn in your homework and exams on WebAssign.   See instructions below to register.

For comments or questions, e-mail me (dcline@stat.tamu.edu) or contact the TAMU Statistics Department.

PDF file of this Syllabus

Course Information

Time and Place: Mon 6:00–7:00, Blocker 411 (Online Question & Answer Session).  Lectures will be provided at the DoStat website.  Please see the instructions below to register (once you get the course codes).
Instructor: Daren Cline, Blocker 459D, 845-1443.   (stat.tamu.edu/~dcline)
E-mail: dcline@stat.tamu.edu
Office Hours: MWF 10:00am–11:00am, or by appointment.  (My Schedule)
Grader: TBA .
hours: TBA.
email: tba@stat.tamu.edu
Class Web Pages: http://www.si-sv2846.com/dostat (DoStat),
https://www.webassign.net/login.html (WebAssign).
Text: John A. Rice, Mathematical Statistics and Data Analysis, 3rd ed. (Duxbury).
Prerequisite: Three semesters of calculus, including multiple integration and a basic understanding of limits.
Homework: Homework will be assigned and collected regularly.  Homework is worth 10% of the total term score.
Please see the homework policy below.
Exams: There will be two midterm exams worth 25% each and a final exam worth 40%.
Please see the exam policy below.
Exam Dates: Exam I: TBA.
Exam II: TBA.
Final Exam: TBA.
Grading Scale: A: 85%–100%.
B: 70%–84%.
C: 60%–69%.
Disabilities Help: The Americans with Disabilities Act ensures that students with disabilities have reasonable accommodation in their learning environment.  If you have a disability and need help, please contact me and Disability Services in B118 Cain Hall, 845-1637.
Academic Integrity: You are expected to maintain the highest integrity in your work for this class.  This includes not passing off anyone else's work as your own, even with their permission.   Please see the homework and exam policies below for specifics.
Copyright: All the resources I provide for this course are copyrighted and may not be copied or distributed without my express, written permission.

Course Policies

Homework Policy: Homework assignments will be downloaded from DoStat.
Homework solutions must be in a single portable document format (PDF) file and uploaded to WebAssign (not DoStat).
You should be identified on the initial page with your TYPED name, course and section number.
Your homework solutions must be your own work, not from outside sources, consistent with the university rules on academic integrity.  I expect you to follow this policy scrupulously.  Your performance on the exams is much more likely to be better.
You may use:
  • Your textbook and notes from class.
  • Your notes, homework, etc., from a related class that you took or are taking.
  • References listed on the syllabus.
  • Discussion with the instructor or grader.
  • Voluntary, mutual and cooperative discussion with other students currently taking the class. There will be an online discussion board.
You may not use:
  • Solutions manuals (printed or electronic).
  • Solutions, notes, homework, etc., from classes taught elsewhere or at another time.
  • Solutions, notes, homework, etc., from students who took the class previously.
  • Copying from students in this class, including expecting them to reveal their solutions in "discussion".
Exam Policy: Distance students must be proctored according to the directions you will be given.
Exams will be downloaded from WebAssign (not DoStat).
Exam solutions must be scanned into a single portable document format (PDF) file only and uploaded to WebAssign.
You should be identified on the initial page with your PRINTED name, course and section number.
Your exam solutions must be your own work, consistent with the university rules on academic integrity.  Distance students must be proctored according to the directions you will be given.
Each exam will be comprehensive and cumulative, and closed book/notes.
I will not expect you to quote theorems and results explicitly but I do expect you to demonstrate that you can make use of them.  Specifically, you will need to:
  • Show all your work.  This does not necessarily mean showing every individual algebraic or calculus step – but it must be clear what those steps are.
  • Identify (by number, name or description) any theorems, examples or homework problems you use.
  • Clearly identify the solution and/or the end of a proof or derivation.
No other resources are acceptable (no calculator).
Copies of old exams will be available for you to review.
Missed Work and Incompletes: This is based on university policy.
  • If you must miss an exam due to illness or circumstances beyond your control, notify me or the Statistics Department, in writing or by email (before, if feasible, otherwise within two working days after you return).  See me as soon as possible to schedule a make-up exam.
  • An Incomplete grade will be given only in the event that circumstances beyond your control cause prolonged absence from class and the work cannot be made up.

The DoStat Website

Students will have access to streaming videos of the lectures at the DoStat website.  All other information for the course also will be accessible on the distance course website.  To access the website, you will need to register according to the instructions below by the time classes start.  The course reference and registration code will be provided to you near the start of the semester.

  1. (If you are already registered as a DoStat user, skip steps 1 and 2 and go to step 3.)  Go to http://www.si-sv2846.com/dostat and click on the Register Here link.
  2. Fill in all of the information and click on Submit.  You should get an email confirming your registration.
  3. Log into http://www.si-sv2846.com/dostat using the information entered in step 2.
  4. Click on the Add Course link to the left.
  5. Fill in the Course Reference DS-XXX and Registration Code XXXXXXX provided to you and press Register.
After registering for the course, take a look at the resources.  Please look/watch for further instructions concerning the use of DoStat, watching videos, attending the Q&A sessions, submission of homework and exams, and using R.
The recorded (streaming video) lectures will be found under "Lectures".  Under "Files" you will find printed lecture notes and examples that are presented in class.  Under "Links" there is an errata sheet for the textbook and a link to the R statistical programming software that will be used to illustrate concepts throughout the course.  (You will need to install R.)

The WebAssign Website

You will turn in your homework for the course at the WebAssign website.  You will also download your exams and submit them at WebAssign.  Register according to the instructions below.  The class key will be provided at the start of the semester.

  1. Go to https://www.webassign.net/login.html and click the I have a class Key button.
  2. Enter in the Class Key and click Submit.
  3. Verify the course section and instructor.  Click YES if it is your course.  If it is not, check with the instructor and try again. \item If you do not have a WebAssign account, select the option I need to create a WebAssign account, fill out the form and click CREATE MY ACCOUNT.
  4. If you already have a webassign account, select the option I already have a WebAssign account and enter your login information.  Be sure to use "tamu" as the Institution value. Click Continue.
After logging in, select the Assignments tab.  This is where you will submit homework and exams and download exams. See the examples provided.  You may submit homework multiple times as long as it is before the due date/time.  Only the last submission will be graded.

Course Outline

Topic Section
1. Introduction to Probability  
A. Interpretation, experiments, sample space, events 1.1--1.2
B. Set theory, definition 1.2--1.3
C. Finite sample spaces, counting methods, combinatorial methods 1.4
D. Conditional probability, Bayes theorem 1.5
E. Independent events1.6
2. Random Variables  
A. Discrete random variables2.1
B. Continuous random variables2.2
C. Important discrete and continuous distributions 2.1--2.2
D. Functions of a random variable2.3
3. Joint Distributions  
A. Discrete random variables3.1--3.2
B. Continuous random variables3.3
C. Independent random variables3.4
D. Marginal and conditional distributions 3.3, 3.5
E. Functions of jointly distributed random variables 3.6
4. Expected Values  
A. Expectation and its properties4.1
B. Moments including mean and variance 4.1--4.2
C. Covariance and correlation4.3
D. Conditional expectations4.4
E. Moment generating functions4.5
5. Limit Theorems  
A. Law of large numbers5.2
B. Central limit theorem5.3
6. Distributions Derived from the Normal Distribution 6.1--6.3
7. Estimation of Parameters and Fitting of Distributions  
A. Parameter estimation7.2--7.3, 8.1--8.3
B. Properties of estimators -- bias, variance, mean squared error 7.3, 8.3, 8.4
C. Method of moments estimators8.4
D. Maximum likelihood estimation8.5
E. Large sample properties of maximum likelihood estimators 8.5
F. Definition of confidence intervals 7.3, 8.5
G. Construction of confidence intervals using pivots
H. Construction of approximate confidence intervals 8.5
 I.  Bayesian inference8.6
J.  Information inequality and efficiency of estimators 8.7--8.8
8. Testing Hypotheses  
A. Bayes approach to testing and the likelihood ratio 9.1, 9.2
B. Basic concepts of hypothesis testing 9.1
C. Neyman-Pearson approach to hypothesis testing 9.2
D. Duality of confidence intervals and tests 9.3
E. Generalized likelihood ratio tests 9.4
F. Wald and score tests
G. Applications of likelihood ratio tests 9.5--9.6

Copyright Information

Each document provided on these web pages is copyrighted by me (Daren B.H. Cline) with all rights reserved, whether or not the document explicitly states so.  These documents may only be used for academic purposes and they may not be reproduced or sold without my permission.  That means you may refer to them for other classes or for research, just as you would any book, as long as neither you nor anyone else reproduces them for sale or other distribution.  If you would like to use some of the material for instruction, you need to first get written permission from me (Daren B.H. Cline, TAMU Department of Statistics, College Station TX 77845-3143).