# the bootstrap

(4.8 hours to learn)

## Summary

The bootstrap is a Monte Carlo technique for estimating variances or confidence intervals of statistical estimators. It uses the empirical distribution as a proxy for the true distribution, and measures the accuracy of the estimator on datasets resampled from the empirical distribution. It is widely applicable and doesn't require assuming a parametric form for the true distribution.

## Context

This concept has the prerequisites:

- expectation and variance (The bootstrap is often used for estimating the variance of an estimator.)
- Monte Carlo estimation (The bootstrap is a Monte Carlo estimator.)

## Goals

- Know the procedures for both the parametric and nonparametric bootstrap
- When would you choose one over the other?
- Note: for the parametric bootstrap, it may help to know about a point estimator such as maximum likelihood , but you can treat this as a black box.

- Be able to use the bootstrap to:
- estimate the variance of an estimator
- compute a confidence interval for an estimator

- The nonparametric bootstrap introduces two sources of error: using the empirical distribution as a proxy for the true distribution, and repeatedly simulating from the empirical distribution. Which of these would you expect to be a larger source of error?

## Core resources (read/watch one of the following)

## -Free-

→ CMU 36-402, Advanced data analysis: the bootstrap

- Section 1, "Stochastic models, uncertainty, sampling distributions," pages 2-4
- Section 2, "The bootstrap principle," pages 4-15
- Section 3, "Non-parametric bootstrapping," pages 15-18

## -Paid-

→ All of Statistics

A very concise introductory statistics textbook.

- Chapter 8, "The bootstrap," pages 107-115
- Section 9.11, "The parametric bootstrap," pages 134-135

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Probability and Statistics

An introductory textbook on probability theory and statistics.

Location:
Section 12.6, "The bootstrap," pages 839-849

## See also

-No Additional Notes-