Statistics 2005-2006

Statistics 2005-2006
M.Phil. course Tinbergen Institute

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 the chapters 2-6, 8, 9 and 14. All together the topics will be treated in 8 lectures. Students are required to study the corresponding theory and examples in the book as well as to make accompanying exercices.

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: 0-534-20934-3

You may also want to see pdf copies of some slides.

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 Mario Bersem (teaching assistant )

Schedule

Wednesdays November 2, 9, 16, 23, 30, December 7, 14 (13.30-16.15). The class on November 30 will start at 12.00 sharp.
Tutorial and assistance with homework usually before the classes.

Place

Tinbergen Institute Amsterdam (see travel directions and map)
Roetersstraat 31
1018 WB Amsterdam
Phone: 020 5513500

Examination

Written exam; you are allowed to use the book and a pocket calculator.
Date and time: December 21, 13.30-16.30.
Place: Room P.016 in the P building (Euclides) of the UvA, Plantage Muidergracht 24 (see map)

Programme

The programme is roughly the same as that of the previous year. The exercises listed below are all useful, but those marked with an asterisk (*) deserve special attention.

Week 1	Rice, chapter 2 Exercises: chapter 2: 3, 5, 13, 21, 23, 27, 33, 41, 44, 53, 55, 59*
Week 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, 37, 38, 55, 57
Week 3	Rice, sections 4.1-4.3 Exercices: chapter 4: 2, 4, 6, 12, 31, 34, 45, 46, 53, 71(a)
Week 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) Exercices: chapter 5: 1, 3, 9, 12, 13, 15, 17, 23, 26
Week 5	Rice, sections 8.3-8.5.2, 8.6 Exercises: chapter 8: 4, 5, 8, 17, 19ab, 39*, 42, 44, 49
Week 6	Rice, sections 8.5.3 (you also read pages 202, 203), 9.1-9.5 Exercises: chapter 8: 52, chapter 9: 1, 2, 3, 5, 7, 9, 12, (15), 18, 21, 22
Week 7	Rice, (you read section 9.4), section 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

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

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