Statistical Inference and Regression Analysis
Professor: William Greene, Stern Departments of Economics and IOMS
BS The Ohio State University, 1972 (Operations Research); MA Wisconsin, 1974 (Economics); PhD Wisconsin, 1976 (Econometrics); History: Cornell 1976-1982; Real world, 1982-1983; Return to ivory tower at Stern (then GBA) NYU, 1983-2008; Toyota Motor Corp Professor, 2007-2011, Robert Stansky Professor, 2012-2017. Publications: Articles - see vita on home page; Books: Modeling Ordered Choices, 2010, Econometric Analysis, 8th Ed (2018); Applied Choice Analysis (2015); Software, NLOGIT (www.nlogit.com), Editor in Chief, Foundations and Trends in Econometrics. Editor in Chief, Journal of Productivity Analysis, Associate editor, Journal of Economic Education, Journal of Choice Modeling, Economics Letters, Journal of Business and Economic Statistics. Research interests: econometric methodology, discrete choice modeling, efficiency and productivity analysis, health economics, transportation, nonlinear estimation, entertainment and media.
Office: MEC 7-90, Ph. 998-0876
Professor: e-mail: email@example.com
Professor: Home Page: http://people.stern.nyu.edu/wgreene
This course has two parts. In the first we will develop topics in mathematical statistics including distribution theory, estimation theory for the method of moments and maximum likelihood estimation, and principles of statistical inference including confidence intervals and hypothesis testing. The second half of the course will examine linear, loglinear and nonlinear regression models. The course is intended to provide background for research and practice in statistical and actuarial science.
I will assume that students are familiar with algebra, calculus, linear algebra and basic probability theory. A prior course in probability and statistics is assumed. The linear algebra will be basic and can be picked up during the course.
Course Requirements and Course Grades
Final grades for the course will be determined on the basis of the following components and weights:
* Homework assignments (details below): (6 @ 3.33%) 20% (in aggregate).
Students may work in groups of up to 4 and submit a single report for the group.
All examinations are open book, open notes, closed telephone. You may bring use tablet if you have your class materials stored on it. Do bring a hand calculator to both exams.
* The text for this course is Hogg, R., McKean, J., and Craig, A;, Introduction to Mathematical Statistics 7th Edition, Pearson, 2013. Labeled HMC below.
* The second half of the course (the sessions
on regression modeling) will draw heavily on Greene, W., Econometric Analysis, Eighth edition, Prentice Hall, 2018. Students
need not purchase this book - access to electronic copies of the relevant
chapters will be provided in class.
Chapters from Greene, Econometric Analysis:
* Some useful notes on several subjects. These include the bare bones theoretical results and lots of examples.
* We will do some computer exercises during the course. Software will be provided (for free) and will be introduced in class.
* Please remember to turn off your cell phone before you come to class.
* Please try to arrive early. Late entrances are disruptive.
* As a general rule, laptops are an annoyance during class, particularly when you are checking your email, playing with Facebook or angry birds, tweeting or watching YouTube videos while others are studying statistics. If you absolutely must use your laptop to take notes, so be it, but you will be asked to submit a copy of your class notes via email within an hour of the end of class.
Course Outline and Schedule
(Thursday 2/8): Probability and distribution theory.
Reading: HMC, Chapters 1.1-1.7, 2.1-2.3, 3.1-3.5
Materials: (Notes 1-Slides: Probability Theory)
Session 2 (Thursday
2/15):Moments, Functions of Random Variables, Covariance and Correlation,
Conditional Moments; Limit Theorems, Law of Large Numbers, Central Limit
Theorem, Asymptotic Distribution.
Materials: (Notes 2-Slides: Moments and Limit Theorems)
Session 3 (Thursday 2/22): Point Estimation; method of
moments, maximum likelihood estimation, Bayesian estimation.
Reading: HMC, Chapters 4.1-4.4, 6.1-6.2, 11.1-11.2.2
Materials (Notes 3-Slides: Estimation Theory)
Session 4 (Thursday 3/1): Normal family of distributions, t, F,
chi-squared; Statistical inference,
point and interval estimation, confidence intervals, bootstrapping
Reading: HMC Chapters 3.4-3.6, 4.2-4.4, 4.9
Materials: (Notes 4-Slides: Inference)
Session 5 (Thursday 3/8):
Hypothesis testing, Neyman-Pearson lemma, likelihood ratio tests, nonparametric
Materials: (Notes 5-Slides: Hypothesis tests)
(Thursday 3/15): NO CLASS (Spring Break)
(Thursday 3/22): MIDTERM EXAM,
Session 6 (Thursday 3/29):
Regression model, part 1.
Materials: (Notes 6-Slides: Regression Part 1)
Session 7 (Thursday 4/5):
Multiple regression model, part 2.
Materials: (Notes 7-Slides: Regression Part 2)
Session 8 (Thursday 4/12):
Multiple regression model, part 3.
Materials: Greene, Chapters 2-4
Materials: (Notes 8-Slides: Regression Part 3)
Session 9 (Thursday 4/19):
Multiple regression model, part 4.
Materials: (Notes 9-Slides: Regression Part 4)
Session 10 (Thursday 4/26):
Advanced topics in regression modeling.
Materials: (Notes 10-Slides: Nonlinear Regression)
(Thursday 5/3): FINAL EXAM
Students may work with one or more of their colleagues on these homework assignments and submit your assignment as a group.
Problem set 1 (due
2/15) Problem set 1
Problem set 2 (due 3/1) Problem set 2 solutions
Problem set 3 (due 3/22) Problem set 3 solutions
Problem set 4 (due 4/5) Problem set 4 solutions
Problem set 5 (due 4/19) Problem set 5 solutions
Data for Problem set 5: Right click to download, left click to launch
(Rice-14_40 minitab) (Rice-14_40 nlogit) (Rice-14_40 Excel)