Afternoon Tutorial 5

The bootstrap is a computer-based approach for calculating the performance of a parameter estimator or a detector. It can also be used to choose an estimator, a detector or a model among a number of candidates. The bootstrap is very useful because with only little in the way of assumptions and modeling it yields more accurate results than Gaussian approximation.

Today, more and more complex statistical models are being introduced in engineering applications that often do not provide satisfactory solutions to many practical problems. In place of the formulae and tables of parametric and non-parametric procedures based on complicated mathematics, tools such as asymptotic approximations or Monte Carlo simulations are often invoked. The problem with Monte Carlo simulations is that they are inapplicable when the underlying distribution is unknown. On the other hand, asymptotic approximations are impractical when the analysis is to be performed with a small set of data. The bootstrap which has revolutionized 1990's statistics, is a remedy for the above problems. It is a method for determining the performance of a parameter estimator or detector and other everyday inferential problems. We believe that the bootstrap will prove useful for many signal processing practitioners.

The purpose of the tutorial is (i) to provide a systematic introduction to the theory of the bootstrap, (ii) to provide guidelines for signal processing practitioners so that "misuse" is avoided in situations where theoretical confirmation is unavailable, and (iii) to stimulate the use of the bootstrap and further developments of resampling techniques. An outline of the tutorial follows. We first introduce bootstrap methods. In particular, we discuss the parametric and the non-parametric bootstrap. We then treat dependent and independent data bootstrap methods and show how they can be used for variance and confidence interval estimation, signal detection, and model selection. Finally, we present some real-life applications. Specifically, we discuss the estimation of the noise floor in radar and confidence intervals for flight parameters from an aircraft's acoustic emission. All examples will be interactively presented using a bootstrap Matlab toolbox. Details can be found at http://www.crcss.qut.edu.au/cip/abdelhak/boot.html.

Dr. Abdelhak M. Zoubir received the Dipl.-Ing. degree (BSc/BEng) from Fachhochschule Niederrhein, Germany, in 1983, the Dipl.-Ing. (MSc/MEng) and the Dr.-Ing. (PhD) degree from Ruhr University Bochum, Germany, in 1987 and 1992, all in Electrical Engineering. From August to December 1983, he was with Klockner-Moeller in Krefeld, Germany. He then joined the Control Division at Siempelkamp AG in Krefeld, Germany, where he was a Consultant until March 1987. From April 1987 to March 1992, he was an Associate Lecturer in the Division for Signal Theory at Ruhr University Bochum, Germany. In June 1992, he joined Queensland University of Technology where he is now Associate Professor in the School of Electrical and Electronic Systems Engineering. Starting March 1999 he will hold the position of Professor of Telecommunications with the Australian Telecommunications Research Institute and the School of Electrical & Computer Engineering at Curtin University of Technology in Western Australia.

His general interest lies in statistical methods for signal processing with applications in communications, sonar, radar, biomedical engineering and vibration analysis. His current research interest is in the area of channel estimation and equalization and the design of detectors in the presence of impulsive interference in digital communications. Dr. Zoubir was the Deputy Technical Chairman (Tutorials & Special Sessions) for ICASSP-94 and the Technical Chairman of the International Symposium on Signal Processing & Its Applications (ISSPA 96). He also served on several technical committees of international conferences. He is Senior Member of the IEEE and Member of the Institute of Mathematical Statistics.

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Last Update:  February 4, 1999         Ingo Höntsch