Advanced Statistics
This course covers concepts in parametric statistics, with a focus on the linear model, as well as nonparametric statistics.
Instructor: Malek Ben Salah
Term: Spring
Course Overview
This course is structured in two chapters: the first chapter is more applied, focusing on the linear model and its practical use, while the second chapter is more theoretical, covering nonparametric estimation.
By the end of this course, you will be able to:
- Build linear models, study them in detail, validate them, select the best model, and perform variable selection
- Construct nonparametric estimators for density and regression functions, and study their properties
Detailed Course Schedule
| Session | Content |
|---|---|
| Lecture 1 (1.5h) | Course organization and grading policy, General introduction, Introduction to Chapter 1: The Linear Model, Parameter estimation and estimator properties |
| Lecture 2 (3h) | Linear model: Distribution of estimators, confidence intervals, and hypothesis testing |
| Lecture 3 (3h) | Linear model: Model validation, model selection |
| Lecture 4 (3h) | Linear model lab session |
| Lecture 5 (3h) | Regularization of linear models (1.5h), Linear model tutorial |
| Lecture 6 (3h) | Nonparametric statistics: Introduction and projection estimators for density |
| Lecture 7 (3h) | Kernel methods for density estimation |