Software help

JMP software is available to students at IIT labs on campus.

Download R, and to read about it, click on the link "What is R"?

Downloadable Books on R: An Introduction to R, by William N. Venables, David M. Smith and the R Development Core Team; Using R for Data Analysis and Graphics - Introduction, Code and Commentary, by John H. Maindonald.
See also Prof. Yang's post on learning R in 15 minutes.

Help with typing math: TeX, etc.

You are encouraged to type your assignments. You can access LaTeX in the computer labs; more information and help can be found on this departmental page. Note: for Macs, I recommend TeXShop.
You might also consider using the what-you-see-is-what-you-get text editor TeXmacs; it makes it unnecessary for you to learn the LaTeX typesetting language while producing output of comparable quality. The program is freely downloadable, available for various platforms, able to import and export LaTeX files, and offers a plugin for certain software packages. Finally, you may just prefer to do things online and not download anything; for that I recommend Overleaf.

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 campuswire to obtain the assigned homework 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 14&16	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 1/21.
January 21&23	Topic 2: Properties of a random sample. Sampling from the Normal distribution. Order statistics. (Time permitting: convergence concepts.)	Section 5.3, 5.4 (and, time permitting, 5.5).	Homework 2, due 1/28postponed.
January 28&30	Topic 2, continued: Convergence concepts: convergence in distribution; CLT; the Delta method. Topic 3, intro: Principles of data reduction.	Sections 5.5, 6.1.	Homework 2, due 2/4.
February 4&6	Topic 3: Principles of data reduction: Sufficiency (sufficient statistics, MSS). Complete statistics. Basu's theorem. Discussion of why sufficiency, model fibers, and sufficient partitions.	Chapter 6 - sections 6.1 and 6.2.	Homework 3, due 2/11.
February 11&13	Topic 4: Point estimation: methods of finding point estimators.	Chapter 7 - 7.1, 7.2: method of moments and MLE. Discussion of the likelihood principle in context of point estimation - read section 6.3 but prepare to not quite believe the likelihood principle (another example provided in lecture). Bayes estimators if time permits; if not, next week.	Homework 4, due 2/18.
February 18&20	Topic 4,continued: Point estimation - methods of finding point estimators - Bayesian point estimator. Topic 5: Point estimation: methods of evaluating estimators - Mean Squared Error, consistency.	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 2/27.
February 25&27	Topic 5,continued Point estimation: methods of evaluating estimators - Best unbiased estimators, efficiency. Lower bounds on variance. Interplay with sufficiency. Consistency of MLE.	Chapter 7 - section 7.3, and Chapter 10 - sections 10.1.1 and 10.1.2.
March 3&5	Topic 5,wrapping up Point estimation: methods of evaluating estimators: Asymptotic optimality / normality of MLE. Topic 6: Introduction to hypothesis testing: the basics of a test, Type I and II errors, level, power, rejection region.	Chapter 10 - sections 10.1.1 and 10.1.2. Chapter 8 - sections 8.1 and 8.3.1. Start of 8.2.	Homework 6, due 3/24 (after spring break, after midterm!).
Mar 10th	Interlude: Various algorithms for parameter estimation. Overview of the EM algorithm; IPF; MCMC-MLE.	Section 7.2.4 and EM handout in class. Additional resources will be provided during this week on Campuswire.	Homework "EM", due 4/30.
Mar 12th	Midterm Exam	Topics: 1-5. The exam will be graded by Friday March 13th.
Mar 17&19	SPRING BREAK.	Catch up on reading from topic 6, wrap up of HW 6, spend time with the EM algorithm assignment. COVID-19 CLASS DISRUPTION: MOVING ONLINE! CHECK HERE OFTEN FOR SCHEDULE UPDATES! CHECK CAMPUSWIRE FOR MOST RECENT INFO!
Mar 24&26	Topic 7: More on hypothesis testing. Plan: More ways to construct tests: Bayesian, Intersection-Union; including the size of UIT and IUT. POST-GOING-ONLINE PLAN: Review setup of hypothesis tests; continue on constructing tests as above. The review will include a shared typed notes on hypotheses tests overview! UPDATE 3/24: Intro to learning online and discussion of related issues. Hypothesis tests setup review. Examples. Discussion of exact vs. asymptotic tests. Discussion of theorem about sufficient statistics and test statistics in the likelihood ratio test. UPDATE FOR 3/26: Asymptoti test for the mean; exact test for the mean under normality; randomized tests; p-values.	Chapter 8, continued. ( 8.3.1, 8.2.3, 8.3.3, 8.3.4.)	Homework 7, due 4/2.
	Mar30 11:59pm CT quiz 1 due [online]
Mar31& Apr2	Topic 7: Hypothesis testing: p-values (continued: p-values of hypothesis tests and two examples including conditioning on sufficient statistic). Methods for constructing tests (Bayesian, UIT,IUT). Time permitting: chi-square test for contingency tables.	We will be skipping around chapter 8 a bit. Sections 8.3.3. and 8.3.4.	Homework 7 due 4/2 and HW 8 due most likely on 4/9.
Apr 7&9	Topic 8: Evaluations of hypothesis tests (including most powerful tests, Neyman-Pearson Lemma, and asymptotics of LRTs). Chi-square test for contingency tables. Discussion of exact vs. asymptotic p-values. [Pointer to "my favorite theorem" talk this month, organized by the SIAM student chapter at IIT; online!]	Section 10.3: Asymptotic distribution of likelihood ratio tests.	Homework 8, due 4/16.
	Apr12 11:59pm CT quiz 2 due [online]
Apr 14&16	Topic 8: Interval estimation	Sections 9.1 and 9.2.2.	Homework 9, due 4/23.
Apr 18&20	Topic 9: 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 4/23.
Apr 25&27	Topic 10: Analysis of variance and regression, an introduction. Catch-up week: finish off last topic; project presentations; early final exam presentations on Thursday (if applicable); etc.	Chapter 11: section 11.2 and 11.3, a few selected topics as overview.	Reminder: Homework EM due 4/30.
Comprehensive Final Exam	Thursday, May 7th, 8:00 am - 10:00 am.	Since we are now online, we will do a differently formatted final exam. Namely, we will be doing a combination of a written take-home exam and a short 5-to-10-minute conversation between each of you and me -- spoken -- where you will get to explain your solution to one of the problems you have already solved live, online. The questions will be assigned at least a week before the exam date.