Math 628: Mathematical Theory of Statistics

MATH 628: Theory of point estimation and hypothesis testing with applications. Confidence region methodologies and relations to estimation and testing.

Professor: Bozenna Pasik-Duncan
Telephone: (785) 864-5162
Email: bozenna@ku.edu



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Homework Grading Policies and Expectations

  1. Weekly assignments of will be collected at the beginning of class each Wednesday. No late HW will be accepted.
  2. The student's name and "Math 628, HW #..." need to be clearly stated on the front page of each submission.
  3. Each problem is worth up to 2 points, with:
    • 0 points for no solution or totally wrong approach
    • 1 point for correct reasoning but the lack of details in justification or/and wrong calculation
    • 2 points for correct reasoning with detailed justification
    Remarks: The focus of this course is on good understanding of mathematical statistics concepts; therefore arithmetic mistakes in this course are negligible, but I require that they be clearly marked. Grading has to be done in such a way that a student will know clearly what was the reason for losing points. Different approaches to finding solutions are encouraged and promoted; therefore looking at posted online solutions while grading students' work is not recommended. I recommend looking at a student's full assignment and providing any general comments or recommendations such as "your presentation requires improvement or significant improvement" at the end of the assignment.
  4. I expect to receive a weekly report/feedback from the grader. In this report I expect to see:
    • the record of points, mean, median, the lowest and the largest value and the standard deviation
    • the list of problems that left students with their concerns; in other words, which problems I should revisit to address students' lack of understanding
  5. Graded assignments will be returned to students in class by the following Wednesday.
  6. At the end of the semester I will expect to receive a cumulative distribution of points and percentages with the same distribution characteristics as for each individual assignment.
  7. Students are responsible for collecting their graded HW assignments and for keeping them in their course portfolio as important evidence of their contributions.

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Homework Assignments

HW # Exercises Due Date
#1 Section 6.1: 7, 8, 9
Section 6.2: 3, 4, 6, 7, 8, 9, 10
2/1/2017
#2 Section 6.4: 1, 2, 4, 5, 6, 8, 9, 10, 11, 12
2/8/2017
#3 Section 6.5: 4, 6, 7
Section 6.7: 1, 2, 3, 4, 5, 6, 7
2/15/2017
#4 Section 7.1: 3, 6, 7, 16
Section 7.2: 3, 10, 12, 14
Section 7.3: 4, 10
2/20/2017
#5 Section 7.3: 11,12
Section 7.4: 3, 4, 7, 8, 12, 14, 15
Section 7.5: 9
3/1/2017
#6 Section 8.1: 3, 6, 7, 10
Section 8.2: 4, 7, 15
Section 8.3: 5, 6, 13
3/8/2017
#7 Section 8.4: 3, 12
Section 8.5: 1, 3, 4
Section 8.6: 2, 3, 5
Section 8.7: 8, 9
3/15/2017
Week of March 20 - 24 - No HW - Spring Break - Enjoy it!
#8 Section 9.1: 1, 2, 3
Section 9.2: 1, 3
4/05/2017
#9 Attached HERE
04/19/2017
#10 Section 6.5: 6, 8
Section 7.6: 10
4/19/2017
#11 Section 9.3: 2, 4
5/1/2017

Lectures

Lecture # Subject Date
#1-5
  • Reviewing different probability distributions, sample mean and sample variance, order statistics, point estimation, unbiased estimators, Cramer-Rao Inequality, efficiency of estimators
January 18-27, 2017
#6-7
  • Maximum Likelihood Estimation
January 30-February 1, 2017
#8-9
  • Methods of Moments, section 6.4
  • Sufficient Statistics, section 6.7
February 6,8 2017
#10
  • Independent study on A simple regression problem, section 6.5
February 10, 2017
#11-13
  • Sufficient Statistics (cont)
  • Confidence Intervals for Means, for the Difference of Two Means, and for the variance: Sections 7.1 & 7.2
  • Confidence Intervals for Proportions, Sec. 7.3
2/13/2017-2/20/2017
#14
  • In class 60 min Exam I
2/22/2017
#15
  • Confidence Intervals for Propertions
  • Sample Size
  • Confidence Intervals for Variance & Ration of Variances
2/24/2017
#16
  • Independent studies - Individual work on redoing Exam I with its focus on very well done presentations of solutions
2/27/2017
#17
  • Introduction to Chapter 8: Tests about one Mean and of the Equality of Two Means, sec. 8.1 & 8.2
3/1/2017
#18
  • Tests about Proportions & the Wilcoxon Tests, sec. 8.3 & 8.4
3/3/2017
#19
  • Tests about Proportions & the Wilcoxon Tests, sec. 8.3 & 8.4 (continuing)
3/6/2017
#20
  • Power of a Statistical Test
3/8/2017
#21 and #22
  • Best Critical regions, Sec. 8.6
3/10/2017 and 3/13/2017
#23 and #24
  • Likelihood Ratio Tests, Sec. 8.7
3/15/2017 and 3/17/2017
#25, 26, 27
  • Likelihood Ratio Tests & Chi-Square Goodness-of-Fit Tests
March 27, 29, 31, 2017
#28, 29
  • Contingency Tables
April 3, 5, 2017
#30, 31
  • Bayesian Estimation
April 7, 10, 2017
#32
  • No Lecture - Independent study- work on HW # 9 & 10.
April 17, 2017
#33
  • Analysis of Variance
April 19, 2017
#34
  • Professor Brian McClendon, Guest Speaker
April 21, 2017
#35, 36, 37
  • Analysis of Variance - Completely Randomized Designs
April 24, 26, 28 2017
#38, 39
  • Introduction to Stochastic Modeling Closing Discussion & Reflections
May 1 and 3 2017