Johannes Jan and Heuchenne Cédric (suppléant)

Downloadable Material

Organization

• 30 hours, 2 hours a week: Tuesday 14:00-16:00, Institut de Statistique.
• The first 1/2 to 2/3 of the course are more traditional (classes, etc...) the last 1/3 to 1/2 will be devoted to presentations of projects (see below) by students, according an agenda to be specified (depending on the number of students).
• Teaching language : English.

Summary

• The course presents the basic techniques of resampling methods (bootstrap, jacknife,. . .) useful in statistics. These methods are now getting more and more popular and present reliable alternatives to traditional asymptotic methods, mostly based on applications of the Central Limit Theorem. The bootstrap offers an attractive alternative in many applications when determining the sampling distribution of a statistics of interest (estimator, test statistics, . . .). In many situations, the quality of the approximation is better than its asymptotic counterpart, while in some others, the asymptotic approximation is not available and the bootstrap turns out to be the only possibility for statistical inference.
• The resampling methods are first introduced in a general framework and their theoretical properties are investigated. Then, keeping in mind that they are first and foremost practical procedures, they are illustrated through many standard problems of statistical inference and concrete statistics and econometrics questions, in order to emphasise the broad range of applications that they apply to.

Objectives

• to use correctly the resampling methods ;
• to understand the underlying mechanisms justifying their use ;
• to use the techniques to solve problems with real data, and to draw appropriate conclusions.

Prerequisites

 

Contents

• Basic ideas of the bootstrap
• Monte-Carlo methods
• Application to basic statistical problems : bias of an estimator, confidence intervals, . . .
• Theoretical properties of the bootstrap
• Hypothesis testing through resampling
• Bootstrap in regression models
• Iterated bootstrap
• The Jacknife
• The smoothed bootstrap
• Bootstrap in time series

Support

• Chernick, M.R. (2008), "Bootstrap methods : a guide for practitioners and researchers", Wiley Series in Probability and Statistics.
• Davison, A.C. and Hinkley, D.V. (1997), "Bootstrap Methods and their Applications", Cambridge University Press.
• Efron, B. and Tibshirani, R.J. (1993), "An Introduction to the Bootstrap", Chapman and Hall.
• Hall, P. (1992), "The Bootstrap and Edgeworth Expansion", Springer.

Evaluation

1. Analysing in a given statistical model the properties of bootstrap estimators of a given characteristic. Simple and direct application of the methods presented in the course, worth 1/3 of the points.
2. Analysing in an original and open theme the properties of bootstrap estimators of some given characteristics of interest, and draw interesting conclusions. Original and inventive exercise, worth 2/3 of the points.