Math 563: Mathematical Statistics
Homework & Lecture Schedule
Homework assignments will be posted at least one week before the due date. It is your responsibility to check the course page on Piazza, which you can also easily access by logging into Blackboard, to obtain the assigned problems.You are expected to start working on the homework sets early (NOT the day they are due or right before). It is extremely difficult to answer last-minute homework questions; particularly if you have not been participating in the Piazza discussion beforehand.
Help with writing up assignments
To improve your mathematical writing quickly, start by writing draft solutions to homework early. A day or two later after you have had time to forget what you wrote, read it. If it doesn’t make sense or convince you, rewrite it. Writing a solution requires saying what you mean and meaning what you say. Be intellectually honest. Intellectual dishonesty includes: 1) stating a “reason” without understanding its relevance. 2) Claiming a conclusion when you know you haven’t proved it. 3) Giving an example and claiming you have proved the statement for all instances.(This text borrowed from Prof. Kaul)
Lecture schedule
You are expected to cover (at least at a high level) the assigned readings before coming to the lecture. This will help you follow the course and organize your notes. In the reading schedule below, all section numbers refer to the course textbook by Casella and Berger.Homework problem sets are naturally related to the material covered in the course; hence, homework numbers are listed next to the corresponding topic.
| Lecture Dates | Tentative topics covered | Assigned reading | Related homework |
| January 11&13 | Topic 1: What is statistical inference and why do we need it? Statistics and sampling distributions. |
Sections 5.1 and 5.2. Review probability as needed (common families of distributions from chapters 3 and 4). |
Homework 1, due 1/20. |
| January 20 | Topic 2: Properties of a random sample. Sampling from the Normal distribution. |
Section 5.3. | Homework 2, due 2/1. |
| January 25&27 | Topic 2, continued: Order statistics, convergence concepts. |
Sections 5.4 and 5.5. | Homework 2, due 2/1. |
| February 1&3 | Topic 3: Principles of data reduction: Sufficiency (sufficient and ancilliary statistics, MSS). |
Chapter 6 - sections 6.1 and 6.2. | Homework 3, due 2/10. |
| February 8&10 | Topic 3, continued: Principles of data reduction: relationship between complete (sufficient) and ancilliary statistics.
Topic 4: Point estimation: methods of finding point estimators. |
Chapter 6 - wrap up 6.2. Chapter 7 - 7.1, 7.2: method of moments and MLE. Discussion of the likelihood principle in context of point estimation - scan section 6.3. Bayes estimators if time permits; if not, next week. |
Homework 4, due 2/17. |
| February 15&17 | Topic 4,continued: Point estimation - methods of finding point estimators - Bayesian point estimator.
Topic 5: Point estimation: methods of evaluating estimators - Mean Squared Error, |
Chapter 7 - section 7.3, and Chapter 10 - sections 10.1.1 and 10.1.2. (Some of these topics may be completed the following week.) |
Homework 5, due 2/29. |
| February 22&24 | Topic 5,continued Point estimation: methods of evaluating estimators - Best unbiased estimators, efficiency. Lower bounds on variance. Interplay with sufficiency. |
Chapter 7 - section 7.3, and Chapter 10 - sections 10.1.1 and 10.1.2. (Some of these topics may be completed the following week.) |
Homework 5, due 2/29. |
| February 29& Mar2 | Topic 5,wrapping up Point estimation: methods of evaluating estimators: Properties of MLEs. Topic 6: Introduction to hypothesis testing: the basics of a test, Type I and II errors, level, power, rejection region. |
Chapter 7 - section 7.3, and Chapter 10 - sections 10.1.1 and 10.1.2. Chapter 8 - sections 8.1 and 8.3.1. Start of 8.2. |
tbd. |
| Mar 7th | Topic 6: Hypothesis testing, continued. | Chapter 8, continued. Likelihood ratio test. | Homework 6, due 3/23. |
| Mar 9th | Midterm Exam | Topics: 1-5. | |
| Mar 14&16 | SPRING BREAK. | Catch up on reading from topic 6. | |
| Mar 21&23 | Topics 6/7: Hypothesis testing, continued. | Chapter 8, continued. Finishing up Likelihood ratio test. More ways to construct tests: Bayesian, Intersection-Union; including the size of UIT and IUT (sections in the book: 8.3.1, 8.2.3, 8.3.3). | Homework 6, due 3/23. Homework 7, due 3/30 OR 4/4. |
| Mar 28&30 | Topic 7: Hypothesis testing: methods of evaluating tests, continued. | Chapter 8, continued: UMP, p-values. On Monday: uniformly post powerful tests and Neyman-Pearson Lemma with proof and example. On Wednesday: UMP based on sufficiency and example; p-values of hypothesis tests and two examples including conditioning on sufficient statistic.
Sections 8.3.3. and 8.3.4. |
Homework 7, due 3/30 OR 4/4. |
| Apr 4&6 | Topic 7: wrap-up of methods of evaluating tests - asymptotic evaluation of LRTs | Finish discussion of p-values as necessary. Section 10.3: Asymptotic distribution of likelihood ratio tests. |
Homework 8, due 4/13. |
| Apr 11&13 | Topic 8: Interval estimation | Sections 9.1 and 9.2.2. | Homework 9, due 4/25. |
| Apr 18&20 | Topic 8: Interval estimation - continued | The first part of sections 9.2.2, 9.3,1, then 9.2.1 and 9.3.2, then 9.2.3, 9.3.3, and finally 10.4. | Homework 9, due 4/27. |
| Apr 25&27 | Topic 9: Analysis of variance and regression, an introduction. | Chapter 11: section 11.2 and 11.3, selected topics. | Homework 9, due 4/27. | Comprehensive Final Exam |
Friday, May 6th, 8:00 am - 10:00 am, RE 102 (same classroom). I will be there at 7am if you want to start early! |