Economics 520: Theory of Quantitative MethodsFall Semester 2010Course SyllabusRevised 8/12/10Lectures: Mon/Wed 2:00–3:15 pm, McClelland 401KKNote: the first four Wednesdays, we will meet in McClelland 122.Instructor: Keisuke Hiranoemail: [email protected] Hours: TBATeaching Assistant: Zaiyan Weiemail: [email protected] hours and review session times to be announcedCourse Description: This course serves as an introduction to probability theory and statistical inference forgraduate studies in economics and related fields. It is particularly intended to prepare students for graduateeconometrics courses (522A and 522B) and for applications of probability theory in other parts of eco-nomics.Prerequisites: You are expected to have taken Economics 519 or to be comfortable with the material cov-ered in that course. More specifically, you are expected to be familiar with multivariable calculus (includingoptimization and Taylor expansions), basic real analysis (set operations, open and closed sets, compact sets,limits, etc.), linear algebra (matrix operations, determinants, etc.), and be comfortable reading and writingmathematical proofs.Textbook:• Casella, G., and Berger, R.L., Statistical Inference, 2nd edition, Duxbury Press.The textbook by Casella and Berger (hereafter CB) is required for the course. I will also provide writtenlecture notes. These are based on notes written by Guido Imbens, and I thank him for permission to adapthis material for this course.You may find it useful to consult other textbooks as you learn this material. I recommend:• DeGroot, M., and Schervish, M., Probability and Statistics, Addison-Wesley.• Severini, T., Elements of Distribution Theory, Cambridge.• Hogg, R., and Craig, A., Introduction to Mathematical Statistics, Prentice Hall.• Silvey, D., Statistical Inference, Chapman and Hall.• Wasserman, L., All of Statistics, Springer.1Assessment:• Homework Assignments 10%: There will be homework assignments nearly every week. They areintended primarily to help you prepare for the exams, and will be graded on a pass/no pass basis.Because of the frequency of the assignments, I will not accept late homeworks for any reason.However, I will drop the lowest homework score when calculating your overall grade in the course.You are allowed to work in groups on the homework, but you must write up your own solutions inyour own words.• Midterm Exam 40%: The (in-class) midterm is tentatively scheduled for Wednesday, October 6 . Wewill finalize the date of the midterm during the first week of classes.• Final Exam 50%: Friday, 12/10/2010, 2:00–4:00 pm. The final exam will be cumulative.Computer Software: Most of the homeworks will involve analytic exercises, but some assignments willalso require you to do some programming. We will use R, a system for statistical computing. It is freelyavailable from http://www.r-project.org/. I will distribute notes on using R, and additional re-sources are available from the R Project website.Course Web Site: http://www.u.arizona.edu/˜hirano/520 2010.htmlI will post lecture notes, homework assignments, and other supplementary material for the course here.Outline: (may be revised as semester progresses)1. Probability Theory(a) Elementary Probability Theory and Combinatorics (CB 1.1-1.2)(b) Conditional Probability and Independence (CB 1.3)(c) Functions of Random Variables (CB 1.4-1.6, 2.1)(d) Expectations (CB 2.2-2.3)(e) Common Distributions (CB 3.1-3.3)(f) Joint distributions, Conditional Distributions, (CB 4.1-4.2, 4.6)(g) Convergence, Laws of Large Numbers, Central Limit Theorem (CB 5.1-5.3, 5.5)2. Statistical Inference:(a) Point Estimation: Method of Moments and Maximum Likelihood (CB 7.1, 7.2.1, 7.2.2)(b) Bayesian Point Estimation (CB 7.2.3)(c) Evaluating Point Estimators (CB 7.3, 6.1-6.2)(d) The Cramer-Rao Bound (CB 7.3)(e) Large Sample Properties of Maximum Likelihood Estimators (CB 10.1.1-10.1.3)(f) Hypothesis Testing (CB 8.1, 8.3.1-8.3.2)(g) Most Powerful Tests (CB 8.3.2-8.3.3)(h) Large Sample Tests (CB 10.3)(i) Confidence Intervals (CB 9.1-9.2,