Statistics (TI1707)
Tinbergen Institute 2022-2023

Contents

The course is intended for students who have a deficiency in probability and statistics. It starts off with the very first principles of probability and quickly passes on to essential statistical techniques. Estimation and testing theory will be reviewed, including maximum likelihood estimators, likelihood ratio test and (least squares) regression. The course is based on John A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press, Belmont, California. From this book we will treat a good deal of the chapters 2-6, 8, 9 and 14. All together the topics will be treated in 7 lectures, of which the first one is a video lecture. Students are required to study the corresponding theory and examples in the book as well as to make accompanying exercises.

In the course we treat the following topics.

Sample spaces, probability measures, distribution functions, random variables with discrete and continuous distributions, functions of random variables, multivariate distributions, random vectors, independent random variables, conditional distributions, functions of random vectors and their distributions, expectation and variance, covariance and correlation, the law of large numbers, central limit theorem, chi-square and t-distributions, estimation, method of moments, maximum likelihood, large sample theory, confidence intervals, Cramer-Rao bound, hypothesis testing, Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, linear regression, least squares estimation of regression parameters, testing regression hypotheses.

Learning objectives

By the end of the course students will be able to:
- understand the principles of probability,
- understand the essential statistical techniques, and
- apply fundamental techniques needed for statistical inference.

Literature

John A. Rice, Mathematical Statistics and Data Analysis, 2nd Edition, Duxbury Press (1995, ISBN: 053420934-3), or 3rd Edition (2007, ISBN: 0534399428). Both editions can be used for this year's course, the new edition has more examples (also from financial statistics) and exercises. For the third edition there is a list of errata. Second hand copies of the book are sometimes available at Amazon Germany. Browse the web for other offers.

Most important are the slides (2020 version) of the first lecture; this lecture will ONLY be presented online. Take notice of these slides before the first lecture on location on August 30, 2022, and also before the first tutorial session.

You may also want to see pdf copies of some slides used in the lectures, or the extra notes complementing some of the material in the book.

Prerequisites

Some knowledge of elementary mathematics. The course Fundamental Mathematics offers more than enough. Basic knowledge of probability is required up to the level of chapter 1 of Rice. This chapter will NOT be treated in the course and students are supposed to be familiar with its contents. Chapter 2 will not be treated in detail, only highlights. Students should study the many examples of distributions themselves.

People

Peter Spreij (lecturer), Fengtao Wan and TA 2 (teaching assistants)

Locations and Schedule

Location: Tinbergen Institute Amsterdam, Gustav Mahlerplein 117, 1082 MS Amsterdam.
Lectures on Tuesdays, 09:00-12:00, starting on 30 August 2022 with Lecture 2. The first lecture will be available online only, links to videos provided by mail to registered participants. You are supposed to know the contents of the online lecture, at least the contents of the slides, before the start of the lectures on location.
TA sessions on Thursdays, 11:30-13:00, starting on September 1.

Examination

Homework assignments and written exam. Homework has to be handed every week on the due dates determined by the TAs. During the written exam you are allowed to use the book and a pocket calculator. Your final grade F will be a weighted average of your result H of the homework assignments and the result E of the written exam: F=0.85*E+0.15*H. Date and time of the written exam: October 19, 2022 As an example of what could be asked, you could have a look at the collection of exam questions.

Interactive website

You may be interested in this interactive website where you can experiment yourself with various topics in probability and statistics. The website accompanies the textbook Statistics: The Art and Science of Learning from Data, 4th Edition by Alan Agresti, Christine A. Franklin, Bernhard Klingenberg. (Thanks to Aisha Schmidt, student who took the course in 2019)

Course Catalogue

Most of the information on this page can also be found in the Course Catalogue of the Erasmus University.

Programme (at most minor changes expected)

The schedule below might see some small changes during the course. Check this page regularly for updates!! The exercises from the book as listed below are all useful, but those marked with an asterisk (*) deserve special attention. During the TA sessions, there may be more emphasis on selected old exam questions than on the listed exercises from the book in the table below. The numbering of the exercises corresponds to the 2nd edition of the book. The numbering of the exercises in the 3rd edition deviates from the numbering in the 2nd edition. We have a conversion table that lists the correspondence between the two editions. It also turned out that the section numbering (sometimes) and page numbering has been changed between the two editions, see the table below.

2nd EDITION3rd EDITION
pages 202-203pages 216-218
section 8.6section 8.7
sections 9.1-9.3sections 9.1-9.2
section 9.4section 9.3
section 9.5section 9.4

FROM WEEK TO WEEK ()
1 Online only! Rice, Chapters 2 and 3 (main themes only); students should study the many examples of distributions themselves, but skip parts of Chapter 3 that require more than basic knowledge of multiple integrals. Detailed contents of the lecture can be found on the slides.
Exercises: Chapter 2: 5, 23, 33, 41, 44*, 53, 55*, 59*; chapter 3: 7, 17(a,b), 32(a), 34*, 37*, 38. There may be some additional exercises by the TA (also in subsequent weeks)!
Homework: none.
2 Rice, Sections 4.1-4.3 (except Markov inequality, but you can read it yourself).
Exercises: Chapter 4: 2, 4, 6, 12, 31, 34*, 46*, 53*, 71(a).
Homework: Chapter 4: 32, 45 (for due data consult the TAs) and read the two slides on dependence and correlation.
Examples of exam questions: 1, 5, 11, 13, 19(a-d).
3 Rice, chapter 5 (skip the considerations involving moment generating functions), sections 6.1, 6.2, 6.3, extra on multivariate normal distributions (see slides).
Exercises: chapter 5: 1*, 3*, 9, 12*, 13, 15, 17*, 23, 26.
Homework: chapter 5: 16, chapter 6: 9 (for due data consult the TAs).
Examples of exam questions: 37(a,e), 40(a,h,i).
4 Rice, sections 8.3-8.5.2
Exercises: chapter 8: 5*(ab), 8, 17*(ab) and (in the numbering of the 3rd!! edition) 5abc, 12 (ignore all questions on Fisher information and on sufficient statistics).
Homework: chapter 8: 14abc, 19ab (for due data consult the TAs).
Examples of exam questions: 10, 15, 16 (ignore parts on theory that has not been treated yet).
5 Rice, sections 8.5.2, 8.5.3, 8.6 (on Cramér - Rao).
Exercises: chapter 8: 39abc*, 42, 44abc, 49.
Homework: chapter 8: 29 (this exercise starts with "Suppose $X_1, X_2,\ldots, X_n$ are i.i.d. $N(\mu, \sigma^2)$ where $\mu$ and $\sigma$ are unknown."), 52; for due data consult the TAs.
Examples of exam questions: 10d, 15d,e, 16e,f.
6 Rice, sections 9.2, 9.3 (confidence intervals and testing), 9.4, 9.5 (very briefly, only mentioned existence of GLR test).
Exercises: chapter 9: 1, 3*, 5, 7*, 9; read the section on the generalized likelihood ratio test for initial, rudimentary understanding only.
Homework: chapter 9: 11, 16 (for due data consult the TAs).
Examples of exam questions: 20, 27.
7 Regression; Rice, sections 9.4 (if not in Week 6), 14.1-14.4 (emphasis on 14.3, 14.4).
Exercises: chapter 9: 15*, chapter 14: 3*, 4, 8*, 9, 12*, 15.
Homework: chapter 14: 5, 16, 25* (for due data consult the TAs).
Examples of exam questions: 8, 18, 24, 39.


To the Korteweg-de Vries Institute for Mathematics or to the homepage of Peter Spreij.