In many signal and information processing applications one is interested in forming estimates of a certain number of unknown parameters of a random process, using a set of sample values. Further, one is interested in finding the sampling distribution of the estimators, so that the respective means, variances, and cumulants can be calculated, or in making some kind of probability statements with respect to unknown true values of the parameters. For example one could be interested in assigning two limits to a certain parameter, and in asserting that, with some specified probability, the true value of the parameter will be situated between these limits, which constitute the confidence interval.
The bootstrap is a powerful technique for assessing the accuracy of a parameter estimator in situations where conventional techniques are not valid. The bootstrap does with a computer what the experimenter would do in practice if it were possible: he or she would repeat the experiment. With the bootstrap, the observations are randomly reassigned, and estimates recomputed. These assignments and recomputations are done thousands of times and treated as repeated experiments.
The Bootstrap Toolbox
The Bootstrap Toolbox is a set of Matlab functions consisting of procedures for resampling, hypothesis testing, and confidence interval estimation. Each function of the Toolbox has a help entry. See the Bootstrap Reference Manual for details.
Examples from an article published in the IEEE Signal Processing Magazine on the application of the bootstrap to signal processing  are also provided. More examples of the application of bootstrap techniques can be found in [2,3,4,5,6].
The Toolbox runs under Matlab 5.0 (or higher) and requires the Statistical Matlab Toolbox, Version 2.1.0 (or higher). Some functions may run under Matlab v4.2c.
The Bootstrap Toolbox has been developed by Abdelhak M. Zoubir and D. Robert Iskander. Hwa-Tung Ong is greatly acknowledged for his help and comments during the development of the Toolbox.
All users of the Bootstrap Toolbox are encouraged to register themselves so they can be notified about upgrades and enhancements.
To register, e-mail: email@example.com with subject line “Bootstrap registration”.
Warranty and Bugs
There is NO WARRANTY attached to this software. If you find that it does not work correctly, please compile a description of the Matlab code that generates the error. E-mail the description to firstname.lastname@example.org. An effort will be made to correct the problem for a future release.
- A. M. Zoubir and B.Boashash, “The Bootstrap and Its Application in Signal Processing”, IEEE Signal Processing Magazine, 15(1):56-76, 1998.
- A. M. Zoubir and D. R. Iskander, “Bootstrapping Bispectra: An Application to Testing for Departure from Gaussianity of Stationary Signals”, IEEE Transactions on Signal Processing, 47(3):880-884, 1999.
- A. M. Zoubir and J. F. Bohme, “Bootstrap Multiple Tests Applied to Sensor Location”, IEEE Transactions on Signal Processing, 43(6):1386-1396, 1995.
- A. M. Zoubir, “Bootstrap Multiple Tests: An Application to Optimum Sensor Location for Knock Detection ”, Applied Signal Processing, 1:120-130, 1994.
- A. M. Zoubir, “Bootstrap: Theory and Applications ”, In F. T. Luk, editor,Advanced Signal Processing Algorithms, Architectures and Implementations, volume 2027, pages 216-235, San Diego, USA, July 1993. Proceedings of SPIE.
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