Generalized Error Control In Multiple Hypothesis Testing
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Author | : Wenge Guo |
Publisher | : |
Total Pages | : 143 |
Release | : 2007 |
Genre | : |
ISBN | : |
Multiple hypothesis testing is concerned with appropriately controlling the rate of false positives when testing a large number of hypotheses simultaneously, while maintaining the power of each test as much as possible. For testing multiple null hypotheses, the classical approach to dealing with the multiplicity problem is to restrict attention to procedures that control the familywise error rate (FWER), the probability of even one false rejection. However, quite often, especially when a large number of hypotheses are simultaneously tested, the notion of FWER turns out to be too stringent, allowing little chance to detect many false null hypotheses. Therefore, researchers have focused in the last decade on defining alternative less stringent error rates and developing methods that control them. The false discovery rate (FDR), the expected proportion of falsely rejected null hypotheses, due to Benjamini and Hochberg (1995), is the first of these alternative error rates that has received considerable attention. Recently, the ideas of controlling the probabilities of falsely rejecting at least k null hypotheses, which is the k-FWER, and the false discovery proportion (FDP) exceeding a certain threshold y have been introduced as alternatives to the FWER and methods controlling these new error rates have been suggested. Very recently, following the idea similar to that of the k-FWER, Sarkar (2006) generalized the FDR to the k-FDR, the expected ratio of k or more false rejections to the total number of rejections, which is a less conservative notion of error rate than the FDR and k-FWER. In this work, we develop multiple testing theory and methods for controlling the new type I error rates. Specifically, it consists of four parts: (1) We develop a new stepdown FDR controlling procedure under no assumption on dependency of the underlying p-values, which has much smaller critical constants than that of the existing Benjamini-Yekutieli stepup procedure; (2) We develop new k-FWER and FDP stepdown procedures under the assumption of independence, which are much more powerful than the existing k-FWER and FDP procedures and show that under certain condition, the k-FWER stepdown procedure is unimprovable; (3) We offer a unified approach for construction of k-FWER controlling procedures by generalizing the closure principle in the context of the FWER to the case of the k-FWER; (4) We develop new Benjamini-Hochberg type k-FDR stepup and stepdown procedures in different settings and apply them to one real microarray data analysis.
Author | : Joseph P. Romano |
Publisher | : |
Total Pages | : 50 |
Release | : 2005 |
Genre | : |
ISBN | : |
Author | : Wenge Guo |
Publisher | : |
Total Pages | : 50 |
Release | : 2017 |
Genre | : |
ISBN | : |
Author | : Sandrine Dudoit |
Publisher | : Springer Science & Business Media |
Total Pages | : 611 |
Release | : 2007-12-18 |
Genre | : Science |
ISBN | : 0387493174 |
This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. These are applied to a range of problems in biomedical and genomic research, including identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments; tests of association between gene expression measures and biological annotation metadata; sequence analysis; and genetic mapping of complex traits using single nucleotide polymorphisms. The procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions, null hypotheses, and test statistics.
Author | : Bernard John Otten |
Publisher | : |
Total Pages | : 554 |
Release | : 1917 |
Genre | : Dogma |
ISBN | : |
Author | : Javier Rojo |
Publisher | : Springer Science & Business Media |
Total Pages | : 1103 |
Release | : 2012-01-16 |
Genre | : Mathematics |
ISBN | : 1461414113 |
These volumes present a selection of Erich L. Lehmann’s monumental contributions to Statistics. These works are multifaceted. His early work included fundamental contributions to hypothesis testing, theory of point estimation, and more generally to decision theory. His work in Nonparametric Statistics was groundbreaking. His fundamental contributions in this area include results that came to assuage the anxiety of statisticians that were skeptical of nonparametric methodologies, and his work on concepts of dependence has created a large literature. The two volumes are divided into chapters of related works. Invited contributors have critiqued the papers in each chapter, and the reprinted group of papers follows each commentary. A complete bibliography that contains links to recorded talks by Erich Lehmann – and which are freely accessible to the public – and a list of Ph.D. students are also included. These volumes belong in every statistician’s personal collection and are a required holding for any institutional library.
Author | : Michael H. Herzog |
Publisher | : Springer |
Total Pages | : 146 |
Release | : 2019-08-13 |
Genre | : Science |
ISBN | : 3030034992 |
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.
Author | : Quan-Lin Li |
Publisher | : Springer Nature |
Total Pages | : 497 |
Release | : 2019-10-21 |
Genre | : Computers |
ISBN | : 981150864X |
This book is dedicated to Jinhua Cao on the occasion of his 80th birthday. Jinhua Cao is one of the most famous reliability theorists. His main contributions include: published over 100 influential scientific papers; published an interesting reliability book in Chinese in 1986, which has greatly influenced the reliability of education, academic research and engineering applications in China; initiated and organized Reliability Professional Society of China (the first part of Operations Research Society of China) since 1981. The high admiration that Professor Cao enjoys in the reliability community all over the world was witnessed by the enthusiastic response of each contributor in this book. The contributors are leading researchers with diverse research perspectives. The research areas of the book iclude a broad range of topics related to reliability models, queueing theory, manufacturing systems, supply chain finance, risk management, Markov decision processes, blockchain and so forth. The book consists of a brief Preface describing the main achievements of Professor Cao; followed by congratulations from Professors Way Kuo and Wei Wayne Li, and by Operations Research Society of China, and Reliability Professional Society of China; and further followed by 25 articles roughly grouped together. Most of the articles are written in a style understandable to a wide audience. This book is useful to anyone interested in recent developments in reliability, network security, system safety, and their stochastic modeling and analysis.
Author | : Alex Dmitrienko |
Publisher | : CRC Press |
Total Pages | : 323 |
Release | : 2009-12-08 |
Genre | : Mathematics |
ISBN | : 1584889853 |
Useful Statistical Approaches for Addressing Multiplicity IssuesIncludes practical examples from recent trials Bringing together leading statisticians, scientists, and clinicians from the pharmaceutical industry, academia, and regulatory agencies, Multiple Testing Problems in Pharmaceutical Statistics explores the rapidly growing area of multiple c
Author | : Houston Nash Gilbert |
Publisher | : |
Total Pages | : 372 |
Release | : 2009 |
Genre | : |
ISBN | : |