Robust Estimation with Applications in Psychophysiological and Biomedical
Statistical signal processing is a powerful area of research that has been successfully applied to generations of research problems in order to extract useful information from empirical data. An effective way to incorporate knowledge about the application at hand is to use parametric models. When applying parametric methods to real-world problems, it often happens that the observations do not exactly follow the assumptions that were made to model the problem. In these cases, the nominally excellent performance can drastically degrade.
This seminar introduces the concept of robust estimation in a way that it is accessible to researchers in the area of psychology. Robust statistics formalize the theory of approximate parametric models. On the one hand, they are able to leverage upon a parametric model, but on the other hand, they do not depend critically on the exact fulfillment of the model assumptions.
The basic concepts and foundations of robust statistical theory are introduced by considering the robust estimation of the location and scale parameters of a univariate random variable. In particular, measures such as the influence function, the breakdown point and the trade-off between robustness and statistical efficiency are discussed.
After laying the foundations using simple models the concepts of robust statistics are extended to more challenging situations. Parameter estimation in linear regression is considered because of its importance of modeling many practical problems. Next, the theory of robust estimation of the multivariate location and scatter (covariance) matrix is introduced and an application of robust regularized discriminant analysis for emotion classification is provided in detail. Finally, correlated data streams, which are commonly measured, e.g., in psychophysiology are treated. A focus will lie on robust parameter estimation for ARMA models as well as methods of robust filtering and outlier cleaning.
During the entire tutorial, ample real-life applications from engineering, bio-medicine and psychophysiology will be given along with information to publicly available implementations of the considered algorithms.