Bootstrap

Date: Monday, 29.7.2019 - Friday 2.8.2019

Topics

• Resampling methods, bootstraps, jacknife, ...
  
  1. Introduction
  2. Parameters, distribution and the plug-in principle
  3. Estimating standard errors
  4. More complicated data structures
  5. Bias
  6. Confidence intervals
  7. Hypothesis testing
  To prepare or to revise, please have a look at the handout:
  

Exercises

Exercises can be found in the handout (datasets are attached to the PDF).

Literature:

• Julian J. Faraway, Extending the Linear Model with R. Chapman & Hall, 2006.
• A. C. Davison, D. V. Hinkley, Bootstrap Methods and their Application, Cambridge University Press, 1997
• Bradley Efron and Robert J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, 1994

Software

For our practical examples (during the entire course) we will use the software environment R. I think that it is helpful to coordinate on one environment. R is free, it is very powerful, and it is popular in the field.

• Documentation for R is provided throught the built in help. You also find support on the R Homepage. You might find the following useful:
  • The R Guide, Jason Owen (Easy to read, explains R with the help of examples from basic statistics)
  • Simple R, John Verzani (Explains R with the help of examples from basic statistics)
  • Einführung in R, Günther Sawitzki (In German. Rather compact introduction.)
  • Econometrics in R, Grant V. Farnsworth (The introduction to R is rather compact and pragmatic.)
  • An Introduction to R, W. N. Venables und D. M. Smith (The focus is more on R as a programming language)
  • The R language definition (Concentrates only on R as a programming language.)
• You can download R from the homepage of the R-project.

  Installing R with Microsoft Windows:

  Download and start the Installer. Install R on your local drive. Installing on a network drive or in the cloud (Dropbox, Onedrive,...) is possible but not recommended.

  Installing R with GNU-Linux:

  Follow the advice to install R for your distribution.

  Installing R with MacOS X:

  Here is a guide to install R with MacOS X.

• In the lecture we use RStudio as a front end.
• We will use the following packages: boot, bootstrap, car, Ecdat, Hmisc, lattice, latticeExtra, lme4, mvtnorm.

  If, e.g., the command library(Ecdat) generates an error message (Error in library(Ecdat): There is no package called 'Ecdat'), you have to install the package.

  Installing packages with Microsoft Windows:

  With RStudio: Use the tab “Install”. Otherwise: Start Rgui.exe and install packages from the menu Packages / Install Packages).

  Installing packages from GNU-Linux or MacOS X:

  From within R use the command install.packages("Ecdat"), e.g., to install the package Ecdat