Description

This course provides a foundation in probability and statistics and introduces basic regression analysis. In probability theory, we cover the basic concepts from probability spaces over random variables up to convergence. This theoretical equipment is needed for inductive statistics and regression analysis that aims at drawing conclusions from samples about causes and regularities underlying the population.
 

Compétences visées

• Familiarity with the basic concepts in probability, statistics, and regression analysis : awareness of theoretical knowledge and first experience in handling and describing data, estimation, and testing using the software R, Stata and Mathematica
• Capacity to compile basic descriptive, and to formulate and test hypothesis about the data generation process, including basic regression analysis

Modalités d'organisation et de suivi

The course includes 30 hours of lecturing (‘cours magistral’). Group exercises need to be handed in on a regular basis. Exercises include pen and paper exercises but also R-programs in which data is analyzed and theoretical concepts are exemplified through simulation. Main teaching materials are the lecture blackboard/slides, textbooks (see Main references), and computer programs in R, Stata and Mathematica.

Detailed content:

• Chapter 1 Elements of Probability Theory

1.1 Some Terminology, 1.2 Definitions of Probability, 1.3 Some Probability Theorems, 1.4 Conditional Probability, 1.5 Independence, 1.6 Bayes’ Rule

• Chapter 2 Univariate Random Variables

2.1 Random Variables and Induced Probability Spaces, 2.2 Discrete Random Variable – PDF and CDF, 2.3 Continuous Random Variable – PDF and CDF, 2.4 Some Remarks On CDFs and PDFs, 2.5 Expectation, Variance and other Properties

• Chapter 3 Multivariate Random Variables

3.1 Multivariate Random Variables, PDFs, and CDFs, 3.2 Marginal Probability Density Functions and CDFs, 3.3 Conditional Density Functions, 3.4 Independence of Random Variables

• Chapter 4 Basic Asymptotics

4.1 Modes of Convergence and the Law of Large Numbers, 4.2 Convergence in Distribution and the Central Limit Theorem

• Chapter 5 Non-parametric density estimation

5.1 Histograms and Kernel Density Estimators, 5.2 Multivariate Density Estimation, 5.3 Kernel Estimation of a Conditional PDF

• Chapter 6 Linear model and OLS

6.1 Introduction, 6.2 Linear Regression Models, 6.3 Least Squares Estimator under Classical Assumption, 6.4 Violations of Classical Assumptions

• Chapter 7 Testing

7.1 Basic Hypothesis Testing Concepts, 7.2 Parametric Hypothesis Tests and Test Properties, 7.3 Tests in the context of the Linear Regression Model, 7.4 Tests of Distributional Assumptions, 7.5 Permutation Tests and the Bootstrap

• Chapter 8 GLMs and the Maximum Likelihood Principle

8.1 Introduction, 8.2 Specification of the Likelihood, 8.3 MLE Properties in Large and Finite Samples, 8.4 Testing in the realm of ML, 8.4 GLM Applications
 

Disciplines

• Sciences économiques
• Sciences de gestion et du management

Bibliographie

• Cameron, A.C. and Trivedi, P.K. (2005), “Microeconometrics: Methods and Applications”, Cambridge University Press, New York.
• Dekking, F.M., Kraaikamp, C., Lopuhaä, H.P., Meester, L.E. (2005) “A Modern Introduction to Probability and Statistics: Understanding Why and How”, Springer-Verlag London Limited.
• Li, Q. and Racine, J.S. (2007), “Nonparametric Econometrics: Theory and Practice”, Princeton University Press.
• Mittelhammer, R.C. (2013) “Mathematical Statistics for Economics and Business, Second Edition”, Springer Science+Business Media New York.
• Schumacker, R., Tomek, S. (2013) “Understanding Statistics Using R”, Springer Science+Business Media New York.