The course will consist of two parts. The first part will introduce the notion of a statistical model and will present the principles of estimation and tests. These principles will be applied to a specific model: the multiple linear model, whose parameters will be estimated using the ordinary least squares method. We will refer wherever possible to concrete examples or simulations to demonstrate the properties of the statistical objects under discussion.
- Reminder of the principal laws of probability.Discrete laws: Bernoulli, Binomial, Pascal, Hypergeometric, Poisson. Continuous laws: Normal law and its derivatives, gamma law
- Introduction to estimation and tests.The model in statistics. Definitions. Free and exhaustive statistics. Introduction to test theory: type I error, type II error, Neyman-Pearson approach. Kolmogorov test, chi squared test, mean equality test.
- Introduction to econometrics.The multiple linear model, the Ordinary Least Squares method, properties of OLS estimators, the Frisch-Waugh theorem, least squares with constraints, finite-distance tests in the linear model.
Wasserman L. (2004) All of Statistics, Springer [21 WAS 00 A]