Math 728: Statistical Theory

MATH 728: The core mathematical statistics topics of estimation, testing, and confidence intervals are covered. Following the core topics such modern topics as ranking and selection procedures, decision theory, nonparametric statistics, regression and ANOVA, and robust statistical procedures are covered. Computer-assisted data analysis is discussed at several points since it is very important for students of modern probability and mathematical statistics to have a comprehensive view that includes a glimpse of the importance of statistical computation to the field.

Professor: Bozenna Pasik-Duncan
Telephone: (785) 864-5162
Email: bozenna@math.ku.edu
Office: 503 Snow Hall

Announcements

  • 5/1/2013:
    See the new Message ("RE: Final remarks") for information about the end of the semester in Math 728.

  • 4/27/2013:
    See the new Message ("RE: Take-home Exam II") for comments on the take-home Exam II that is due in class on 4/30/13.

  • 4/11/2013:
    See the new Message ("RE: Writing Assignment") for information on the writing assignment that is due on 4/16/13.

  • 4/9/2013:
    To learn more about Jerzy Neyman and his contributions to statistics, see "The Legacy of Jerzy Neyman," written by Dominique Duncan as the final paper for the History of Statistics class (2007) taught by Professor S. Stigler at the University of Chicago.

  • 4/8/2013:

  • 4/6/2013:
    Please note the following important additions to the Message "RE: Final Project, part 2."
    • The abstract must be no longer than 100 words.
    • The subject must be selected from the course textbook so that the focus of the paper lies within the scope of Math 728.
    • The paper cannot be taken from another course or another project (meaning that you cannot receive a double credit for this work).

  • 4/5/2013:
    See the new Message ("RE: Final Project, part 2") for more information about the Final Project.

  • 3/27/2013:
    See the new Message ("RE: Final Project") for a partial list of topics for the Final Project.

  • 3/6/2013:
    • The HW#4 deadline has been postponed until Tuesday, 3/12/13.
    • The student-designed samples of Exam I have been posted under Resources.
    • See the new Message ("RE: Exam I") for important details about Exam I and about receiving full credit for the student-designed sample exams.

  • 3/3/2013:
    On Tuesday, 3/5/13, the class will work in groups on designing Exam I. The exam will be the result of collaborative effort of all students. On Tuesday please bring to the class the following items: your textbook, graded HW#1 and HW#2 (HW#3 will be returned in class), and draft of the solutions to HW#4 (it is recommended that you work on HW#4 before Tuesday's class).

  • 2/26/2013:
    The HW#3 deadline has been postponed again, until Thursday, 2/28/13.

  • 2/25/2013:
    KU Mathematics faculty candidate Terry Soo from University of Victoria will present "Equivariant Constructions in Probability and Ergodic Theory" at 4:00 p.m. on Tuesday, 2/26/13, in 306 Snow Hall. In the event of campus closure, the talk will be moved to 1:00 p.m. on Wednesday.

  • 2/21/2013:
    The HW#3 deadline has been postponed until Tuesday, 2/26/13. Enjoy the snow!

  • 2/7/2013:
    Nobel laureate and financial economist Robert Merton will present "A Next-Generation Solution for Funding Retirement: A Case Study in Design and Implementation of Financial Innovation" at 1 p.m. on Friday, 2/15/13 at the Dole Institute of Politics. Merton received the Nobel Prize in Economics in 1997 for his work on the Black-Scholes-Merton model for pricing options. This model remains one of the best ways to determine the value of derivative securities, and it is considered one of the most important concepts in modern financial theory.

  • 2/5/2013:
    Workshop I has been posted below as an Extra Credit assignment due Wednesday, 2/6/2013.

  • 1/31/2013:
    Homework 1 has been posted below and is due in one week. Please note that all homework problems will be taken from the 7th edition of the textbook unless otherwise specified.

  • 1/25/2013:
    Nathan Welch's Excel spreadsheet from Thursday, 1/24/13, is now posted under Supplements as "Example Distribution Generator."

  • 1/22/2013:
    Welcome to Math 728!  Stay up to date with course annoucements and assignments by checking this webpage regularly throughout the semester.

Messages



Resources



Supplements

Homework Assignments
HW # Exercises Due Date
#1 Problems 4.1.2, 4.1.6, 4.4.5, 4.4.9, 5.1.2, 5.1.3, 5.2.1 from the 7th edition of the textbook.

Students with the 6th edition may refer to this problem sheet.

Here is Formula 4.1.9., used in Problem 4.1.6.

Some of the problems do appear in the 6th edition, but are numbered differently as follows.
Thanks to the student who provided this list!

6th Ed               7th Ed
None                 4.1.2
None                 4.1.6
5.2.5                 4.4.5
5.2.9                 4.4.9
4.2.2                 5.1.2
4.2.3                 5.1.3
4.3.1                 5.2.1

HW#1 Solutions prepared by Peter Lewis.
HW#1 Solutions prepared by Nathan Foster.		 2/7/2013
#2 Problems 4.2.1, 4.2.12, 4.2.17, 4.2.18, 4.2.21, 4.2.22, 4.2.27 from the 7th edition of the textbook.

Students with the 6th edition may refer to this problem sheet.

Some of the problems do appear in the 6th edition, but are numbered differently as follows.

6th Ed                 7th Ed
None                   4.2.1   
5.4.7                   4.2.12
5.4.12                 4.2.17
5.4.14                 4.2.18
4.4.19                 4.2.21
4.4.20                 4.2.22
4.4.25                 4.2.27

HW#2 Solutions prepared by Josh Dean.
HW#2 Solutions prepared by Guo Chen.
HW#2 Solutions prepared by Logan Godkin.		 2/14/2013
#3 Problems 4.5.8, 4.5.9, 4.5.10, 4.5.13, 4.6.4, 4.6.5, 4.6.7, 4.6.8, 4.6.9, 4.6.10 from the 7th edition of the textbook.

These problems do appear in the 6th edition, but are numbered differently as follows.

6th Ed                 7th Ed
5.5.8                   4.5.8   
5.5.9                   4.5.9   
5.5.10                 4.5.10 
5.5.13                 4.5.13 
5.6.4                   4.6.4   
5.6.5                   4.6.5   
5.6.7                   4.6.7   
5.6.8                   4.6.8   
5.6.9                   4.6.9   
5.6.10                 4.6.10 

HW#3 Solutions prepared by Josh Dean.
HW#3 Solutions prepared by Aleks Pavlenko (note that: "There's a blank space in problem 4.5.9 which I left to draw the power function graph by hand").		 2/28/2013
#4 Problems 4.7.1, 4.7.3, 4.7.4, 6.1.2, 6.1.4, 6.1.9, 6.2.1 from the 7th edition of the textbook.

These problems do appear in the 6th edition, but are numbered differently as follows.

6th Ed                 7th Ed
5.7.1                   4.7.1   
5.7.3                   4.7.3   
5.7.4                   4.7.4   
6.1.3                   6.1.2   
6.1.5                   6.1.4   
 6.1.10                 6.1.9    
6.2.1                   6.2.1   
 3/12/2013
#5 Problems 6.2.3, 6.2.7, 6.2.8, 6.2.9, 6.2.12, 6.3.1, 6.3.8 from the 7th edition of the textbook. 3/28/2013
#6 Problems 7.2.4, 7.2.5, 7.2.6, 7.3.3, 7.4.1, 7.4.2, 7.4.3 from the 7th edition of the textbook.
(The problems are the same in the 6th edition.)		 4/4/2013
#7 Problems 8.1.1, 8.1.2, 8.1.3, 8.1.4, 8.1.5, 8.2.4, 8.2.5 from the 7th edition of the textbook.
Read Section 8.1 and be prepared for discussion on:
The importance of the Neyman-Pearson Lemma and Jerzy Neyman and his contributions to statistics. 		4/16/2013
#8
(last HW)		 Problems 11.2.1, 11.2.2, 11.2.3, 11.2.4, 11.2.5 , 11.2.8, 11.2.9 from the 7th edition of the textbook. 4/23/2013

Extra Credit
Ex. Cr. # Exercises Due Date
#1 Workshop I.

Best individual or group presentations with complete solutions submitted by midnight CT on Wednesday, February 6 will receive 10 extra credit points. 		2/6/2013

Lectures
Lecture # Subject Date
#1
  • Introduction to Mathematical Statistics - Overview
1/22/2013
#2
  • Special Distributions: Gamma, Chi-square and Beta (Sec. 3.3), t- and F- (Sec. 3.6)
 1/24/2013
#3
  • Chapter 4 - Some Elementary Statistical Inferences:
  • Sampling and Statistics - Unbiased Estimators (Sec. 4.1)
 1/29/2013
#4
  • Order Statistics - Review (Sec. 4.4)
  • Maximum Likelihood Estimator, Rao-Cramer Inequality, Efficiency (Sec's. 4.1, 6.1, 6.2)
 1/31/2013
#5
  • Convergence in Probability, Convergence in Distribution, Central Limit Theorem (Sec's. 5.1, 5.2, 5.3)
 2/5/2013
#6
  • Confidence Intervals (Sec's. 4.2, 4.3)
  • Turn in HW#1 and HW#2 TBA
2/7/2013
#7
  • Confidence Intervals - continuation (Sec's. 4.2, 4.3, 4.5)
 2/12/2013
#8
  • Introduction to Hypothesis Testing (Sec's. 4.5, 4.6, 4.7)
  • Turn in HW#2 and HW#3 TBA
2/14/2013
#9
  • Chi-Square Tests (Sec. 4.7)
 2/19/2013
#10
  • Maximum Likelihood Estimation and Rao-Cramer Lower Bound and Efficiency
  • Short Quiz on Confidence Intervals and Testing Hypotheses (see HW# 2 and 3)
  • Turn in HW#3 and HW#4 TBA
2/28/2013
#11
  • Revisiting Maximum Likelihood Estimation (Sec. 6.1)
  • Rao-Cramer Lower Bound and Efficiency (Sec 6.2)
  • Maximum Likelihood Tests (Sec. 6.3)
 3/5/2013
#12
  • In class Exam I based on HW 1, 2, 3, 4
  • Turn in HW#4 and HW#5 TBA
3/7/2013
#13
  • Asymptotic Efficiency and Asymptotic Relative Efficienc (Sec. 6.)
 3/12/2013
#14
  • Maximum Likelihood Tests (Sec. 6.3)
  • Introduction to Sufficiency (Sec's. 7.1, 7.2)
 3/14/2013
#15
  • A Sufficient Statistic for a Parameter (Sec's. 7.2, 7.3)
 3/26/2013
#16
  • Sufficiency - continuation (Sec's. 7.4, 7.5)
  • Turn in HW#5 and HW#6 TBA
 3/28/2013
#17
  • Sufficiency - Functions of sufficient statistics and jointly sufficient (Sec's. 7.6, 7.7)
  • Review Sec's. 7.1 - 7.4
 4/2/2013
#18
  • The exponential class of distributions (Sec. 7.5)
  • Turn in HW#6 and HW#7 TBA
 4/4/2013
#19
  • Optimal Tests of Hypotheses (Sec's. 8.1, 8.2)
 4/9/2013
#20
  • Optimal Tests of Hypotheses (Sec. 8.3)
 4/11/2013
#21
  • Bayesian Statistics (Sec's. 11.1, 11.2)
  • Workshop on Chapter 8
  • Turn in HW#7
 4/16/2013
#22
  • Bayesian Statistics - continuation (Sec. 11.2)
 4/18/2013
#23
  • Workshop on Chapter 11
  • Applications of Statistics to Real World Problems: Analysis of Variance, Regression Analysis
  • Turn in HW#8
 4/23/2013
#24
  • Applications of Statistics to Real World Problems (continuation): Data Modeling
  • Take-Home Exam II. Turn in on Tuesday, April 30
4/25/2013
#25
  • Data Analysis
  • Turn in Take-Home Exam II
 4/30/2013
#26
  • Summary: What did we learned well in this class? Discussion
  • Presentations of Summaries of the Final Papers.
 5/2/2013
#27
  • Working on the Final Papers & Presentations of the Summaries of the Final Papers.
 5/7/2013
#28
  • Working on the Final Papers & Presentations of the Summaries of the Final Papers.
 5/9/2013