Resampling Methods

Objectifs

Use your knowledge of probability and inferential statistics to define a resampling method suited to the inference under consideration.
Implement a resampling method
Read and discuss a scientific text using resampling methods for statistical purposes.

Plan

Statistical inference generally relies on knowledge of the probability distributions of statistics. If the distribution of a statistic is unknown, a resampling method uses Monte Carlo simulation to approximate this distribution conditionally on the observed data. The principle of this technique is to substitute an empirical distribution constructed from the training sample for the unknown probability law.
The aim of this course is to present the main resampling methods: permutation testing, cross-validation, jackknife and bootstrap. The course will alternate descriptions of procedures, mathematical proofs, exercises and practical case studies. The course will focus on independent and identically distributed statistical models. As time goes by, we’ll look at extensions of the Bootstrap applied, for example, to heteroscedastic models (Wild Bootstrap), dependent data (Block Bootstrap, Subsampling) or massive data (Bag of Little Bootstrap).
1.permutation testing
2.cross-validation and jackknife
3.the Efron Bootstrap
4. Pathological cases and time dependence
A list of uncorrected exercises is provided to enable students to practice in addition to the lectures.

Prérequis

probability, inferential statistics, regression, supervised learning, time series, Bayesian computation