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More Specific Signal Detection in Functional Magnetic Resonance Imaging by False Discovery Rate Control for Hierarchically Structured Systems of Hypotheses
Signal detection in functional magnetic resonance imaging (fMRI) inherently involves the problem of testing a large number of hypotheses. A popular strategy to address this multiplicity is the control of the false discovery rate (FDR). In this work we consider the case where prior knowledge is available to partition the set of all hypotheses into disjoint subsets or families, e. g., by a-priori knowledge on the functionality of certain regions of interest. If the proportion of true null hypotheses differs between families, this structural information can be used to increase statistical power. We propose a two-stage multiple test procedure which first excludes those families from the analysis...
Simultaneous Statistical Inference
This monograph will provide an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate (FDR) and related error measures, particularly addressing applications to fields such as genetics, proteomics, neuroscience and general biology. The book will also include a detailed description how to implement these methods in practice. Moreover new developments focusing on non-standard assumptions are also included, especially multiple tests for discrete data. The book primarily addresses researchers and practitioners but will also be beneficial for graduate students.
Basics of Modern Mathematical Statistics
This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious study or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.
