Title: Recent Advances on Bootstrap for Signal Processing
The use of more accurate models in signal processing applications such as communications, radar, sonar, biomedical engineering, speech and image processing and machine learning has become a fundamental requirement. With an improved accuracy the models have become more complex and inferential statistical signal processing required in parameter estimation, signal detection and classification, for example, has become intractable. The signal processing practitioner requires a simple but accurate method for assessing errors of estimates and answering inferential questions. Asymptotic approximations are useful only when enough data is available, which is not always possible due to time constraints, the nature of the signal or the measurement setting. In place of the formulae and tables of parametric and non-parametric procedures based on complicated mathematics and asymptotic approximations, tools such as the bootstrap are powerful for solving complex engineering problems. It is the method of an engineer's choice for solving inferential signal processing problems, such as signal detection, confidence limits estimation and model selection, to mention a few. In this talk, we first give a brief overview of the basic principle underlying the bootstrap methodology. We then discuss bootstrap techniques for independent data, followed by bootstrap techniques for dependent data. Bootstrap methods for signal detection and model selection are presented along with frequency domain bootstrap methods for spectral analysis. Real-data examples are given throughout the talk.