statistics-resampling

Statistical analysis using resampling methods
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Updated 25 May 2024

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Documentation

Package maintainer

Andrew Penn (andy.c.penn@gmail.com)

Package contributors

Andrew Penn
(More contributors are welcome!)

Citations

If you use this package, please include the following citation(s):

(Note that package versions 5.4.3 and below were named the 'statistics-bootstrap' package. The 'statistics-resampling' package is a more developed version of the older 'iboot' package).

Description

The statistics-resampling package is an Octave package and Matlab toolbox that can be used to perform a wide variety of statistics tasks using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and calculate p-values for null hypothesis significance tests. Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures.

Using the statistics-resampling package online

Try out the statistics-resampling package in your browser at statistics-resampling-online : a ready-to-go implementation of statistics-resampling in a JupyterLab Notebook with an Octave kernel. Note that the first time (since the last repository commit) that you use statistics-resampling online with Binder you can expect it to take a while to build a docker image, but subsequent access to statistics-resampling-online will take less than a minute or so.

Collaborative student projects in GNU Octave can use the statistics-resampling package at Octave-Online. Doing so requires users to download the latest release of the Source code (tar.gz) from here and follow steps 2-5 of these instructions.

Users who prefer Jupyter and have a workflow that is collaborative and/or crosses over multiple programming languages may find it more convenient to install and use the statistics-resampling package at COCALC. The approach described above (for Octave-Online) also applies to installing the statistics-resampling package via a Jupyter Notebook with an Octave kernel at COCALC.

Alternatively, if you have an account with MATLAB you can try out the statistics-resampling package at Matlab-Online Open in MATLAB Online by either following the local installation instructions below, or by adding the toolbox (not collection) version of the package via Apps >> Get More Apps.

Follow the links in the 'Quick start' section below to obtain some examples of data and code to try out with the package.

Requirements and dependencies

Users with greater computational demands may want to consider installing and running the statistics-resampling package offline. Installation of the statistics-resampling package has some software requirements. The core functions in this package require, and are known to be compatible with, GNU Octave (version >= 4.4.0) and Matlab (version >= R2007a 7.4.0). Some optional features of this package have further dependencies:

Installation

To install (or test) the statistics-resampling package in your computer at a location of your choice, for either Matlab or Octave, follow these steps:

  • Download the latest package release from here. Extract (not just browse) the contents of the compressed file (.zip or .tar.gz), and move the package directory to the desired location.
  • Open Octave or Matlab (command prompt).
  • Change directory (cd) into the package folder. (The directory contains a file called 'make.m' and 'install.m', among others)
  • Type make to compile the MEX files from source (or use the precompiled binaries if available. If suitable precompiled binaries are not available for your platform, then Matlab/Octave will need access to a C++11 compiler. Note that if you skip the make step, then the package functions will still work, but some will run slower. This step is interactive so check the command window.)
  • Type install. The package will load now (and automatically in the future) when you start Octave/Matlab.

If you want or need to uninstall the package, change directory (cd) into the package folder and type uninstall.

Alternatively, Octave users can install the latest release of the package just like any other Octave package by typing:

pkg install -forge statistics-resampling

Or for the most recent developmental version of the package:

pkg install "https://github.com/gnu-octave/statistics-resampling/archive/refs/heads/master.zip"

The package can then be loaded on demand in Octave with the following commmand:

pkg load statistics-resampling

(Note that this isn't necessary if you used the local installation instructions first described in this section)

Alternatively, MATLAB users can conveniently install the package functions as a toolbox by double-clicking the 'statistics-resampling.mltbx' file in the matlab subdirectory. The toolbox installed in this way can be disabled or uninstalled via MATLAB's Add-On manager. MEX files are included with the toolbox installation for Windows (32- or 64-bit), MacOS (Intel or Apple Silicon 64-bit) and Linux (64-bit).

Usage

All help and demos are documented on the 'Function Reference' page in the manual. If you do not see the navigation pane on the manual web pages, please enable javascript in your browser. If you need further help with using any of the functions in this package, please post your questions on the discussions page.

Function help can also be requested directly from the Octave/MATLAB command prompt, by typing help function-name - substituting in the actual function name.

In Octave only, you can get a basic overview of the package and it's functions by typing: pkg describe -verbose statistics-resampling, or request demonstrations of function usage by typing demo function-name. Users can also request help with using functions and programming in Octave at the discourse group.

TIPS: You can now document and publish your statistics-resampling analysis in Jupyter Notebooks (with an Octave kernel) at your GitHub repository using the nbgitpuller link generator and the statistics-resampling-online Binder environment . Alternatively, you could fork the repository or use it as a template for you own GitHub repository. Using Jupyter notebooks, you can also integrate use of the statistics-resampling package into your analysis workflow alongside other programming languages including Python, R and Julia

Quick start

Below are links to demonstrations of how the bootstrap or randomization functions from this package can be used to perform variants of some commonly used statistical tests, but without the Normality assumption:

For examples of how to import data sets from a human-readable text file, like a tab-separated-value (TSV) and comma-separated-value (CSV) file, see the examples in the JupyterLab Notebook at statistics-resampling-online and the last demonstration listed on this page

Issues

If you find bugs or have any suggestions, please raise an issue on GitHub here. If you have any problems specifically with Binder for statistics-resampling online, please raise an issue on GitHub here. Please make sure that, when reporting a bug, you provide as much information as possible for other users to be able to replicate it.

Package: statistics-resampling

Cite As

Penn, Andrew Charles. Resampling Methods for Small Samples or Samples with Complex Dependence Structures [Https://Github.com/Gnu-Octave/Statistics-Resampling/]. Zenodo, 2020, doi:10.5281/ZENODO.3992392.

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Version Published Release Notes
5.5.17

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.17

5.5.16

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.16

5.5.15

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.15

5.5.14

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.14

5.5.13

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.13

5.5.12

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.12

5.5.11

See release notes for this release on GitHub: https://github.com/gnu-octave/statistics-resampling/releases/tag/5.5.11

5.5.10

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5.5.9

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5.5.7

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5.5.6

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5.5.4

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5.5.2

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5.5.1

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5.5.0

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5.4.4

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5.4.3

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5.4.2.0

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5.4.1.0

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5.4.0.0

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5.3.5.0

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5.3.3.0

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5.3.2.0

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5.3.1.0

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5.3.0.0

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5.2.8.0

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5.2.7.0

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5.2.6.0

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5.2.5.0

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5.2.4.0

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5.2.3.0

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5.2.2.0

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5.2.1.0

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5.2.0.0

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5.1.6.0

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5.1.5.0

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5.1.4.0

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5.1.3.0

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5.1.2.0

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5.1.1.0

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5.1.0.0

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5.0.2

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5.0.1

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5.0.0

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4.2.0

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4.1.1

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4.1.0.0

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4.0.0.0

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3.10.2.0

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3.10.1.0

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3.9.3.0

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3.9.2.0

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3.9.1.0

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3.8.1.0

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3.8.0.0

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3.7.16.0

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3.7.15.0

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3.7.14.0

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3.7.13.0

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3.7.12.0

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3.7.11.0

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3.7.10.0

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3.7.9.0

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3.7.8.0

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3.7.7.0

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3.7.6.0

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3.7.5.0

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3.7.4.0

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3.7.3.0

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3.7.2.0

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3.7.1.0

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3.7.0.0

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3.6.10.0

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3.6.9.0

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3.6.8.0

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3.6.7.0

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3.6.6.0

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3.6.5.0

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3.6.4.0

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3.6.3.0

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3.6.2.0

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3.6.1.0

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3.6.0.0

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3.5.1.0

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3.5.0.0

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3.4.0.0

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3.3.9.0

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3.3.8.0

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3.3.5.0

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3.3.4.0

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3.3.2.0

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3.3.1.0

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3.3.0.0

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3.2.4.0

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3.2.2.0

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3.2.1.0

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3.2.0.0

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3.1.7.0

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3.1.6.0

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3.1.5.0

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3.1.4.0

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3.1.3.0

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3.1.2.0

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3.1.1.0

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3.1.0.0

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3.0.3.0

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3.0.2.0

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2.9.2.0

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2.9.1.0

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2.9.0.0

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2.8.8.0

Set random seed to make ibootci deterministic when running in serial mode. modified code to make computation of random permutations the same between Matlab and Octave. Updated DOI for all versions

2.8.7.5

Corrected citation

2.8.7.4

Updated citation

2.8.7.3

added DOI to citation

2.8.7.2

Corrected bug in double block bootstrap: Second block bootstrap resampling no longer samples across the block joints of the first bootstrap sample sets.

2.8.7.1

Fixed bug that prevented calculation of BCa intervals for Block bootstrap and made calculations of acceleration constant (for BCa intervals) erroneous for bootstrapping clustered data.

2.8.7.0

Added BCa intervals for all types of bootstrap sampling (ordinary, weighted, block, cluster etc.). Bug fix for cluster bootstrap resampling. Added parallel computing capabilities for Octave. Subfunctions moved into function files in iboot package.

2.8.4.2

Now includes bias-corrected percentile intervals

2.8.3.5

Added the option for smoothing the bootstrap to improve interval coverage for small smples. Removed BCa type intervals since these can be unreliable for small samples.

2.8.1.0

Parallel implementation of ibootci now works for all resampling options (with the only difference being that the first level bootstrap uses ordinary resampling with replacement instead of balanced resampling)

2.8.0.0

Added support for accelerating calculations by performing computations in parallel across CPUs. Made calculations of design effect optional.

2.7.9.6

Minor bug fix for DEFF calculation after Block and Cluster bootstrap.

2.7.9.4

Now includes a new optional input argument 'stderr' for provision of a function handle to calculate standard errors for Studentized intervals (instead of using bootstrap iteration). Also includes minor bug fixes.

2.7.9.0

Minor changes to syntax to provide backwards compatibility back to R2007A

2.7.6.0

For cluster resampling option, balanced resampling now occurs at the level of cluster means. Resampling now used to estimate design effect across the full range of input options. Minor bug fixes.

2.7.0.0

Wild bootstrap removed since it is now superseded by pairs bootstrap, which is implemented with double bootstrap and is compatible with block resampling. Corrected bootidx output argument for block resampling.

2.6.0.0

Now includes an option to perform Wild bootstrap, compatible with BCa intervals but not bootstrap iteration. Output structure includes autocorrelation results to examine the assumption of i.i.d.

2.5.0.0

Improved algorithm for block bootstrap. Now combines circular, overlapping blocks with the double bootstrap approach of Lee and Lai (2009); the calibration method makes interval coverage less sensitive to the choice of block length.

2.4.0.0

Added capability for block bootstrap of dependent data (e.g. time series)

2.3.7.0

Improved the coverage of cluster bootstrap for unbalanced cluster sizes.

2.3.4.0

Trimmed output structure down to providing only necessary information

2.3.2.0

Corrected calculation of ICC for output structure S

2.3.0.0

Now includes capability to perform two-stage nonparametric bootstrap sampling with shrinkage correction for clustered data

2.2.2.0

Made calculation of SSE components of stratified data (provided as descriptive statistics in output structure S) compatible with multivariate data. Now also returns the degrees of freedom.

2.2.0.0

Changed default interval type to BCa to be consistent with bootci. Corrected some comments and function help.

2.1.0.1

Added extra tags to the webpage

2.1.0.0

Now supports calculation confidence intervals using the bootstrap-t method. Standard errors of the bootstrap samples are determined by double bootstrap.

2.0.0.0

This new version can also perform stratified bootstrap resampling.

1.9.0.0

If bootstrap iteration is requested, bootstat returns: boostat statistics from both 1st and 2nd bootstrap; the double bootstrap bias and bias-corrected statistic in S; and, the double boostrap corrected standard error of the statistic in S.

1.8.4.0

Added a check for successful calculation of the acceleration constant for the BCa intervals

1.8.3.0

Corrected the check for when bootstrap confidence intervals hit the ends of the bootstrap distribution

1.8.2.0

Updated title and summary

1.8.1.0

Linked to Github

1.8.0.0

Moved to Github. Calibration and interval construction carried out by interpolating from the empirical distribution function. Minor performance improvement by avoiding a sort in the second bootstrap. Coverage confirmed with simulations.

1.7.1.0

Performance enhancement for the second bootstrap through alternative execution of randperm

1.7.0.0

Included error message when second bootstrap replicate size is insufficient for the desired alpha. Minor improvement to the calibration included. Changed output arguments: Now includes output structure (of settings and results) and calibration curve.

1.6.3.0

Added back a warning for when the resulting intervals hit the end(s) of the bootstrap distribution

1.6.2.6

Corrected typos (missing % signs) in the comments of the examples in the description

1.6.2.5

Updated image icon

1.6.2.4

Adjusted icon image dimensions

1.6.2.3

Adjusted icon image dimensions

1.6.2.2

Adjusted icon image size

1.6.2.1

Minor update to function description. Added image icon.

1.6.2

Swapped the order of output arguments to match Matlabs bootci

1.6.1

Set default bootstrap type to percentile.

1.6

Added the ability to use different types of intervals: percentile or BCa. The BCa type interval is the default.

1.5.4.2

Made minor changes to the description and to the function help

1.5.4.1

Corrected description

1.5.4.0

Added the capability to use bootidx input when calculating bootstrap confidence for multivariate data. Modified default values for nboot

1.5.3.3

Clarified some of the help/comments and included another example of it's usage for calculating confidence intervals for the median

1.5.3.2

Updated some comments

1.5.3.1

Modified default values for the number of bootstrap samples

1.5.3.0

Modified the implementation with weights based on simulation results

1.5.2.1

Updated the help comments

1.5.2.0

Fixed a bug preventing some function usage. Added back the ability to use functions (in the bootfun input argument) that do not output a row vector for matrix input argument(s) (e.g. 'corr' function).

1.5.1.1

Removed depreciated lines of code

1.5.1.0

Implemented appropriated weight allocation for the second bootstrap

1.5.0.0

Added interpolation also to the first bootstrap. Performance improvements made to the resampling algorithm. Added feature to provide weights to modify sampling probabilities.

1.4.1.0

Corrected a mistake presented in example 3 (in comment only).

1.4.0.0

1.4.0.0 - Implementation modified for less memory footprint. Algorithm now uses balanced resampling. Coverage is calibrated using the interpolation method instead of the approximate Monte Carlo method. Also returns bias of the bootstrap.

1.3.0.0

Simplified title
Included example usage in the function help

1.2.0.0

Now less stringent data requirements. Data can be row vectors or column vectors

1.1.0.0

Now checks the dimensions of the data

1.0.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.