Department of Economics
University of California - Davis
Professor Colin Cameron
SSH Building 1124
Tues-Thurs 1.40 - 3.00 pm Wellman 001
Discussion To be arranged. Most likely Friday.
Wednesday 2.00 - 3.30 pm
Thursday 9.00 - 10.20 am
Pre-requisites: Upper division undergraduate sequence in
probability and statistics, econometrics and linear algebra.
NOTE: IF YOU HAVE NOT DONE AN UPPER DIVISION UNDERGRADUATE SEQUENCE IN PROBABILITY AND STATISTICS THEN YOU WILL FIND MUCH OF THE MATERIAL NEW AND SHOULD GET A LOWER LEVEL STATISTICS TEXT (LISTED BELOW) IN ADDITION TO THE COURSE TEXT.
Course Outline: Draft.
1. Introduction to Probability and Statistics
2. Probability Theory HMC 1.1-1.2 (Slides 1)
3. Probability Theory continued HMC 1.3-1.4 (Slides 1)
4. Random Variables, distributions, transformations, expectations HMC 1.5-1.10 (Slides 2)
5. Commonly-used distributions HMC 3.1-3.4,3.6 (Slides 2)
6. Bivariate distributions and transformations HMC 2.1-2.2 (Slides 3)
7. Bivariate distributions, conditional distributions and conditional expectations HMC 2.3-2.5 (Slides 3)
8. Multivariate distributions HMC 2.6-2.7 (Slides 3)
9. Multivariate distributions HMC 2.8, 3.5 (Slides 3)
10. Statistical Inference Introduction: Sampling, Statistics, Estimation HMC 4.1 (Slides 4)
11. Midterm exam
12. Statistical Inference Introduction: Confidence Interval HMC 4.2-4.3 (Slides 4)
13. Statistical Inference Introduction: Hypothesis Tests HMC 4.5-4.6 (Slides 4)
14. Monte Carlo procedures HMC 4.8-4.9 (Slides 5)
15. Convergence in Probability, law of large numbers HMC 5.1 (Slides 6)
16. Convergence in Distribution, central limit theorem HMC 5.2-5.4 (Slides 6)
17. Maximum Likelihood: Point estimation HMC 6.1 (Slides 7)
18. Maximum Likelihood: Efficiency HMC 6.2 (Slides 7)
19. Maximum Likelihood: Hypothesis Testing HMC 6.3 (Slides 7)
20. Brief discussion: Point estimation: Sufficiency HMC 7.1-7.5 (Slides 8)
20. Brief discussion: Hypothesis Tests: Most powerful tests HMC 8.1-8.3 (Slides 9)
Course slides available at Canvas.
Text: Hogg, McKean and Cragg (2013), Introduction to Mathematical Statistics, Seventh Edition, Pearson.
Much of the class will follow this book. The book is often more detailed than what will be covered in this class.
The book is more advanced than an undergraduate text and has
relatively few real data examples. It is "mathematical
statistics" not "statistics".
I very strongly recommend also having an undergraduate probability and statistics text that presents material more simply and with more examples.
Two such books are
Robert V. Hogg and Elliot Tannis, Probability and Statistics, Pearson.
Richard Larson and Morris Marx, Introduction to Mathematical Statistics and its Applications.
The older the edition the cheaper the book.
The most commonly-used Ph.D. level text is Casella and
Berger (2002), Statistical Inference, Second Edition, Duxbury.
This is more advanced than Hogg, McKean and Cragg.
Assignments will include both theory and data examples using
STATA is available on both Econ and ARE computers (http://www.ssds.ucdavis.edu/computing/computing).
If you choose to purchase Stata go to http://www.stata.com/order/new/edu/gradplans/student-pricing/ Get the Stata/IC version.
To get started see http://cameron.econ.ucdavis.edu/stata/stata.html
Course material will be posted at http://canvas.ucdavis.edu
Best 6 out of 7. Last assignment is compulsory. Each worth 3%.
Due Tuesdays October 10, 17, 24, Oct 31, November 14, 21, and Thursday December 7.
Thursday November 2 in class
Tuesday December 12 1.00 - 3.00 pm Comprehensive.
must be handed in on time, so solutions can be discussed in
class and distributed in a timely manner.
No credit for late assignments. Lowest assignment score is dropped.
Academic integrity is required. What is academic integrity? See the UCD Student Judicial Affairs website http://sja.ucdavis.edu/cac.html
As an exception to their rules, I permit some collaboration with other students in doing assignments, but the work handed in must be your own. Each person must create their own Stata output and write up their own answers. And you are to write on your assignment the name of the person(s) you worked with.
Exams will be closed book. The final exam is comprehensive.