Resampling methods with applications
[STAT3210]
[30h] 5 credits
This course is taught in the 1st semester.
Teacher(s): Gery Geenens
Language: English
Main themes
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.
Content and teaching methods
in statistics. Those 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.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
A good knowledge of basic statistical inference is preferable.
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:
- Handout :
Simar, L. (2008), An Invitation to the Bootstrap : Panacea for Statistical Inference ?, Institut
de Statistique, UCL. Available on-line.
Other references include :
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
The students are asked to prepare a report on a personal project. This project comprises two parts :
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.
A list of prospective projects, with guidelines, will be provided at the first class. The report should be ±15 pages, and should be handed in by a certain date, fixed by the professor at the first class.