# Bootstrap and Resampling Methods

#### LAPENTA Elia

Department: Economics

### 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)

### References

• Davison, A. C., & Hinkley, D. V. 1997. Bootstrap Methods and their Application. Cambridge

University Press.

Efron, Bradley, & Tibshirani, R. J. 1994. An Introduction to the Bootstrap. CRC Press.

Horowitz, Joel L. 2001. The Bootstrap. In: Handbook of Econometrics, Chapter 52. Elsevier.

Politis, Dimitris N., Romano, Joseph P., & Wolf, Michael. 1999. Subsampling. Springer-Verlag.

Shao, Jun, & Tu, Dongsheng. 1995. The Jackknife and Bootstrap. Springer-Verlag.

van der Vaart, A. W. 2001. Asymptotic Statistics. Cambridge University Press.

Van der Vaart, A. W., & Wellner, Jon. 1996. Weak Convergence and Empirical Processes : With

Applications to Statistics. Springer-Verlag.