Review of bootstrap principles and coverage analysis of bootstrap confidence intervals for common estimators
This project was developed in Autumn 2019 as part of my master thesis for the MSc in Statistics at ETH Zurich.
The bootstrap is a statistical technique that has been around for 40 years since it was introduced by Efron (1979). Its use in practice is widespread, but many practitioners do not fully understand its limits and under which circumstances it works or does not work. This thesis tries to address this issue, first by exploring the theoretical underpinnings of the bootstrap and then by analysing its performance in some practical scenarios for common estimators.
- Chapter 1 starts with an introduction to the bootstrap, its fundamental principles and how it works.
- Chapter 2 gets into when the bootstrap works (consistency) and when it does not, and if it works at which rate it does so (accuracy).
- Chapter 3 explores a number of first- and second-order accurate bootstrap confidence intervals, introduces a general technique to improve bootstrap intervals called double bootstrap and presents the two most well-known R packages to implement the bootstrap.
- Chapter 4 illustrates the results from a coverage analysis of bootstrap intervals in different scenarios for the sample mean, sample median and sample (Pearson) correlation coefficient, computed via simulations.
- Chapter 5 makes a summary of the thesis and presents a list of conclusions.
- Chapter 6 outlines interesting points and topics to explore further.
The code available in this repository has been used to run the simulations for Chapter 4: Coverage Analysis of Bootstrap CIs for Common Estimators.
MIT License.