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