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title: "Introduction - The Bootstrap"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575339/Introduction%20-%20The%20Bootstrap"
format: markdown
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# **The Bootstrap**

The Bootstrap (sometimes called *Resampling*) was introduced by [Efron (1979)](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26579303) and is explored in great depth and very readably in both [Efron and Tibshirani (1993)](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26579303) and [Davison and Hinkley (1997)](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26579303). It is an extremely flexible technique belonging to the [classical](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575342/) school of statistics.

 

<span style="color: #000000">This section presents a brief introduction covering the main aspects of the bootstrap. Key reasons for the popularity and usefulness of the bootstrap are:</span>

 

1. It is easy to perform using Monte Carlo simulation methods;
2. It corresponds well with traditional techniques where they are available, particularly when a large data set has been obtained; and
3. It offers an opportunity to assess the uncertainty about a parameter (especially when multiple parameters are correlated) where more traditional classical statistics techniques are not available.

 

  


**[The Jacknife](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575404/)**

 

The precursor to the Bootstrap

 

##### [The non-parametric Bootstrap](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575405/)

The non-parametric Bootstrap is used to estimate parameters of a population or probability distribution when we do *not* know the distributional form, which is the most common situation.

 

Example:

[Estimate of population mean, standard deviation and other statistics](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575409/)

 

##### [The parametric Bootstrap](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575406/)

The parametric Bootstrap is used to estimate parameters of a population or probability distribution when we believe we know the distributional form (e.g. Normal, Lognormal, Gamma, Poisson, etc).

 

Examples:

[Estimate of prevalence](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575408/)

[Estimate of Poisson intensity](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575411/)

[Estimate of population mean, standard deviation and other statistics](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575410)

 

 

**[Bootstrap likelihood function](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575418/)**

 

Using the Bootstrap as a likelihood function in Bayesian inference

 

 

**[Estimating parameters for multiple variables](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575419/)**

 

We are sometimes interested in estimating parameters that describe relationships between variables, for example: regression parameters and rank correlation coefficients. The Bootstrap can provide uncertainty about these estimates in an intuitive way, by Bootstrapping the paired data values.

 

Examples:

[Estimate of least squares regression parameters](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575417/)

[Difference between two population means](https://epixanalytics.atlassian.net/wiki/spaces/EA/pages/26575414/)

 

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