Bootstrap Applications and other Resampling methods


Objective

The aim of this course is to present the basic techniques of resampling methods (bootstrapping, jackknifing etc.). These methods have developed considerably in recent years as alternatives to the usual asymptotic methods. Asymptotic methods are based on applications of the central limit theorem. In problems with various applications, bootstrap methods offer an alternative to determining the sampling distributions of particular statistics. This makes it possible to resolve standard inference problems (estimator bias, confidence intervals, hypothesis tests, prediction) even in complex situations (parametric and non-parametric models). These methods will be presented in theoretical terms and then applied to the standard models in statistics and econometrics (linear model, chronological series etc.). The methods make intensive use of the calculating power of computers. The course will also mention other more specific estimation methods based on simulation techniques.

Planning

  1. Introduction to the basic principles of bootstrapping
  2. Monte Carlo method
  3. Estimating the bias of an estimator
  4. Confidence intervals (different methods)
  5. Hypothesis tests (calculating p-values etc.)
  6. Theoretical properties of bootstrapping
  7. Bootstrapping in regression models (including prediction)
  8. Iterated bootstrapping
  9. Various application subjects: (chronological series, smoothed bootstrap, jackknifing etc.)
  10. Other simulation-based estimation methods (simulated moments or maximum likelihood)

Références

  • Efron, Bradley ; Tibshirani, Robert J. An introduction to the bootstrap. Monographs
    on Statistics and Applied Probability, 57. Chapman and Hall, New York, 1993.
  • Wasserman, Larry. All of nonparametric statistics. Springer Texts in Statistics. Sprin-
    ger, New York, 2006.
  • Politis, Dimitris N. ; Romano, Joseph P. ; Wolf, Michael. Subsampling. Springer
    Series in Statistics. Springer-Verlag, New York, 1999.
  • Romano, Joseph P. ; Wolf, Michael. Exact and approximate stepdown methods for
    multiple hypothesis testing. J. Amer. Statist. Assoc. 100 (2005), no. 469, 94-108.
  • Giraud, Christophe. Introduction to high-dimensional statistics. Monographs on Sta-
    tistics and Applied Probability, 139. CRC Press, Boca Raton, FL, 2015.