Bootstrap and Resampling Methods

Objectif

This course has several goals: (i) introducing the general principles of resampling under different forms (bootstrap, subsampling, cross-validation, permutation); (ii) applying the resampling methods to different statistical/econometric contexts (e.g. asymptotic or not, parametric and nonparametric models, regression models, instrumental variables models); (iii) presenting the mathematical theory behind the main results. The practical performance of the resampling methods will be explored through Monte Carlo simulations and real data applications. The programming language used will be R.

Plan

1. The general principles of bootstrapping. When the bootstrap is useful and when it is more attractive than the asymptotic approximation. The Jackknife. Permutation tests.

2. Applications to (semi) parametric models, models with exogenous regressors, models with endogeneity.

3. Applications to nonparametric and semi-nonparametric models.

Références

• 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.