Robust Sequential Analysis

• Applicant: Professor Dr.-Ing. Abdelhak Zoubir
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 390542458

Sequential Analysis is concerned with statistical inference when the number of samples is not given a priori, but is increasing over time. The design goal is to minimize the average number of samples required to fulfill constraints on the reliability and/or accuracy of the inferred quantities. Sequential procedures have been shown to significantly reduce the average number of samples compared to equivalent fixed-sample-size procedures and find application in fields as diverse as medical diagnosis, environment monitoring, quality control, hazard detection, image processing, and spectrum sensing.The idea underpinning robust statistics is to sacrifice some efficiency under nominal conditions in order to be less sensitive to deviations from the ideal case. Hence, robust procedures are designed to perform well in a neighborhood of the assumed model, typically allowing for small, but arbitrary deviations. In this sense, robust methods form the middle ground between parametric and nonparametric approaches.The idea of this project is to combine the benefits of sequential and robust statistics: Sequentially performing a robust procedure compensates the loss in nominal efficiency. Robustly performing a sequential procedure reduces its sensitivity to model mismatch.The two main goals of the project are as follows. First, we want to develop a concise theoretical framework for robust sequential analysis that unifies detection and estimation. We conjecture that the same mathematical tools that we developed in previous work to characterize the minimax solution of sequential binary hypothesis tests can be applied to multiple hypotheses as well as joint detection and estimation. More precisely, we expect the minimax optimal stopping and decision policy to be determined by the solution of a Fredholm integral equation and the corresponding least favorable distributions to be determined by a state dependent family of f-dissimilarities.The second goal is the development of practical algorithms. Again, we aim for a unified approach that can be applied to all well-defined inference problems. We further want to avoid strict assumptions about the underlying applications and distributions, but instead focus on the common mathematical structure of the problems. Consequently, the two central tasks for implementing robust sequential procedures are to solve Fredholm integral equations and to minimize f-dissimilarities over convex sets of distributions.Bringing together two main areas of expertise of the Signal Processing Group, the project will be based on a solid foundation of existing work and experience. The Signal Processing Group is internationally recognized for its work on robust estimation and has made notable contributions to robust and sequential detection in recent years. Therefore, we see ourselves in a uniquely favorable position for a successful completion of the proposed project.

• DFG Programme: Research Grants