Statistics 2009-2010
M.Phil. course Tinbergen Institute

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. 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.

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, found by Leontine Treur. Second hand copies of the book are sometimes available at Amazon Germany. Browse the web for other offers.

You may also want to see pdf copies of some slides. NEW: On December 9, I updated the extra notes with properties of the least squares estimator in regression models.

Prerequisites

Some knowledge of elementary mathematics. The course Mathematics 1 by Jan Brinkhuis 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.

People

Peter Spreij (lecturer) and Xiaoyu Shen (teaching assistant)

Locations and Schedule

Although part of the M.Phil. programme of the Tinbergen Institute, the lectures are not given at Roetersstraat 31, 1018 WB Amsterdam, but at different nearby locations. Lectures mostly on Wednesday afternoons, but not on November 25. Additional lecture on Thursday November 5, first lecture on October 28. TA sessions irregular. Consult the tables for the exact schedule. By clicking on the addresses, you'll find maps and travel indications.

lecturedatetimelocation
1Wed 28 Oct 200914:00-17:00 Mauritskade 57, room 0.20
2Wed 04 Nov 200915:00-18:00Plantage Muidergracht 14 (Euclides, P-building), room P.017
3Thu 05 Nov 200914:00-17:00Roetersstraat 15 (A-building), room A4.04
4Wed 11 Nov 200915:00-18:00Valckenierstraat 65-67 (JK-building), room JK 3.88
5Wed 18 Nov 200915:00-18:00Valckenierstraat 65-67 (JK-building), room JK 3.88
6Wed 02 Dec 200915:00-18:00Valckenierstraat 65-67 (JK-building), room JK 3.88
7Wed 09 Dec 200915:00-18:00Roetersstraat 15 (A-building), room A 4.06

TA sessiondatetimelocation
1Thu 29 Oct 200911:00-12:00 Plantage Muidergracht 14 (Euclides, P-building), room P0.20
2Wed 04 Nov 200918:00-19:00Plantage Muidergracht 14 (Euclides, P-building), room P.017
3Thu 05 Nov 200917:00-18:00Roetersstraat 15 (A-building), room A4.04
4Thu 12 Nov 200916:15-17:15TBA
5Thu 19 Nov 200911:00-12:00Plantage Muidergracht 14 (Euclides, P-building), room P0.20
6Thu 03 Dec 200911:00-12:00Plantage Muidergracht 14 (Euclides, P-building), room P0.20
7Thu 10 Dec 200911:00-12:00Plantage Muidergracht 14 (Euclides, P-building), room P0.20

Examination

Homework assignments and written exam. Homework has to be handed in every two weeks on a Wednesday, see the schedule below. 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=(3E+H)/4.
Date and time of the written exam: December 16, 13:30-16:30, at the Tinbergen Institute Rotterdam, room TBA. Don't forget to bring your copy of Rice, you need it for consulting a table.
As an example of what could be asked, you could have a look at the exams of December 21, 2005 and June 30, 2006.

Programme

The programme will be roughly the same as that of the previous year, to be found below. Check this page regularly for updates!! The exercises listed below are all useful, but those marked with an asterisk (*) deserve special attention. 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 list 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 Rice, chapter 2
Exercises: chapter 2: 3, 5, 13*, 21, 23, 27*, 33, 41, 44*, 53, 55*, 59*
2 Rice, sections 3.1-3.4, 3.6 (not all details, skip parts that require more than basic knowledge about multiple integrals)
Exercises: chapter 3: 1, 3, 7, 14(a)*, 17(a,b), 32(a), 34* (treated during class), 37*, 38, 55*, 57
Homework: chapter 3: 8(a,b), 19 (due date November 18)
3 Rice, sections 4.1-4.3
Exercises: chapter 4: 2, 4, 6, 12, 31, 34*, 45*, 46*, 53*, 71(a)
Homework: chapter 4: 32, 45 (due November 18)
4 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 (due December 2)
5 Rice, sections 8.3-8.5.2, 8.6
Exercises: chapter 8: 4*, 5*, 8, 17*, 19ab*, 39abc*, 42, 44abc, 49
Homework: chapter 8: 14abc, 19ab (due December 2)
6 Rice, sections 8.5.3 (you also read pages 202, 203), 9.1-9.3
Exercises: chapter 8: 52*, chapter 9: 1, 2, 3*, 5, 7*, 9, 12*, 15, 18, 21, 22, read section 9.4 and pay special attention to the second half of page 302 (on p-value) as well
Homework: chapter 9: 11, 16 (due December 16)
7 Rice, sections 9.4, 9.5 (very briefly), sections 14.1-14.4
Exercises: chapter 9: 15*, chapter 14: 1, 3*, 4, 8*, 9, 11, 20, (24), 25*, 31
Homework: chapter 14: 5, 16 (due December 16)


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