statistics-bootstrap

Estimate bias, uncertainty (standard errors and confidence intervals) and test hypotheses (p-values) using bootstrap resampling.

This package of functions can be used to estimate bias, uncertainty (standard errors and confidence intervals) and test hypotheses (p-values) using bootstrap resampling. Variations of the bootstrap are included that improve the accuracy of bootstrap statistics for small samples [1-9].

(This file exchange submission was formally the ibootci function).

Recommended functions from this package include:

• boot returns resamples data or indices created by balanced bootstrap or bootknife resampling
• bootknife performs balanced bootknife resampling and calculates bootstrap bias, standard error and confidence intervals. The interval types supported are simple percentile, bias-corrected and accelerated, or calibrated percentile. This function supports iterated and stratified resampling.
• bootnhst calculates p-values by bootstrap null-hypothesis significance testing (two-tailed). This function can be used to compare 2 or more (independent) samples in designs with a one-way layout. This function resamples under the null hypothesis.
• bootmode uses bootstrap to evaluate the likely number of real modes in a distribution
• bootci is a function for calculating bootstrap confidence intervals. This function is a wrapper of the bootknife function but has the same usage as the bootci function from Matlab's Statistics and Machine Learning toolbox.
• bootstrp is a function for calculating bootstrap statistics. This function is a wrapper of the bootknife function but has the same usage as the bootstrp function from Matlab's Statistics and Machine Learning toolbox.

At the Octave/MATLAB command prompt, type help function-name for more information about the function and it's input and output arguments.

For samples with complex dependence structures, please consider using the legacy iboot package instead at https://github.com/acp29/iboot

bootci and bootstrp are provided in this package because the equivalent functions in MATLAB's Statistics and Machine Learning Toolbox contain a couple of errors, namely in the calculation of the bias for `cper` and `bca` intervals, and in the calculation of `stud` intervals.

Installation

To install (or test) the statistics-bootstrap package at it's existing location in either Octave or Matlab, follow these steps:

• Download the package. If it is a compressed file, decompress it.
• Open Octave or Matlab command prompt.
• cd to the package directory. (The directory contains a file called 'make.m' and 'install.m')
• Type make to compile the mex files from source (or use the precompiled binaries if available).
• Type install. The package will load now (and automatically in the future) when you start Octave/Matlab.

To uninstall, cd to the package directory and type uninstall.

Bibliography

[1] Hesterberg T.C. (2004) Unbiasing the Bootstrap: Bootknife Samplingvs. Smoothing; Proceedings of the Section on Statistics & the Environment. Alexandria, VA: American Statistical Association.

[2] Davison et al. (1986) Efficient Bootstrap Simulation. Biometrika, 73: 555-66

[3] Gleason, J.R. (1988) Algorithms for Balanced Bootstrap Simulations. The American Statistician. Vol. 42, No. 4 pp. 263-266

[4] Efron (1987) Better Bootstrap Confidence Intervals. JASA, 82(397): 171-185

[5] Efron, and Tibshirani (1993) An Introduction to the Bootstrap. New York, NY: Chapman & Hall

[6] Hall, Lee and Young (2000) Importance of interpolation when constructing double-bootstrap confidence intervals. Journal of the Royal Statistical Society. Series B. 62(3): 479-491

[7] Ouysee, R. (2011) Computationally efficient approximation for the double bootstrap mean bias correction. Economics Bulletin, AccessEcon, vol. 31(3), pages 2388-2403.

[8] Davison A.C. and Hinkley D.V (1997) Bootstrap Methods And Their Application. Chapter 3, pg. 104

[9] Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, http://arxiv.org/abs/1411.5279