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Multiple Testing Procedures And Simultaneous Interval Estimates With The Interval Property
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Book Synopsis Multiple Testing Procedures and Simultaneous Interval Estimates with the Interval Property by : Yingqiu Ma
Download or read book Multiple Testing Procedures and Simultaneous Interval Estimates with the Interval Property written by Yingqiu Ma and published by . This book was released on 2012 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of step-wise multiple testing procedures arises because single step procedures are extremely conservative. Research into the construction of useful, computationally feasible interval estimates corresponding to step-wise procedures has been slow. We present an alternative method of constructing multiple testing procedures that easily admits corresponding interval estimates. The new approach has the desirable interval property not usually shared by step-wise procedures. Furthermore, the new method take dependency into account and easily carried out. In addition, these intervals are typically shorter, less likely to contain the null point falsely, and are more informative than those based on traditional methods. Applications include treatments vs control, change point and all pairwise comparisons. Examples and simulations are included.
Book Synopsis Handbook of Multiple Comparisons by : Xinping Cui
Download or read book Handbook of Multiple Comparisons written by Xinping Cui and published by CRC Press. This book was released on 2021-11-18 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows. Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values. Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement. Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9. Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Book Synopsis Multiple Comparisons and Multiple Tests Using SAS, Second Edition by : Peter H. Westfall
Download or read book Multiple Comparisons and Multiple Tests Using SAS, Second Edition written by Peter H. Westfall and published by SAS Institute. This book was released on 2011 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and extensively updated for SAS 9 and later, this work provides cutting-edge methods, specialized macros, and proven best bet procedures. The book also discusses the pitfalls and advantages of various methods, thereby helping readers to decide which is the most appropriate for their purposes. 644 pp. Pub. 7/11.
Book Synopsis Simultaneous Confidence Intervals Using the Restriced Scheffe Method and Sequential Testing Procedures for Single-step Methods by : Yimin Zhang
Download or read book Simultaneous Confidence Intervals Using the Restriced Scheffe Method and Sequential Testing Procedures for Single-step Methods written by Yimin Zhang and published by . This book was released on 2014 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple comparison problems arise when a set of inferences are considered simultaneously. When a separate inference approach is used to answer multiple related questions, it can cause many false positives and lead to erroneous conclusions. Multiple comparison procedures are used to deal with this issue and properly control for multiplicity through some joint measure of erroneous inference. A plethora of measures for error rates, as well as many methods addressing them, have been developed, although in this dissertation, we restrict our attention to familywise error rate (FWE), the probability of making at least one false positive among all the hypotheses.
Book Synopsis Multiple Testing Problems in Pharmaceutical Statistics by : Alex Dmitrienko
Download or read book Multiple Testing Problems in Pharmaceutical Statistics written by Alex Dmitrienko and published by CRC Press. This book was released on 2009-12-08 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Multiple Comparisons Using R by : Frank Bretz
Download or read book Multiple Comparisons Using R written by Frank Bretz and published by CRC Press. This book was released on 2016-04-19 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at http://CRAN.R-project.org After giving examples of multiplicity problems, the book covers general concepts and basic multiple comparisons procedures, including the Bonferroni method and Simes’ test. It then shows how to perform parametric multiple comparisons in standard linear models and general parametric models. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey’s all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. The last chapter reviews other multiple comparison procedures, such as resampling-based procedures, methods for group sequential or adaptive designs, and the combination of multiple comparison procedures with modeling techniques. Controlling multiplicity in experiments ensures better decision making and safeguards against false claims. A self-contained introduction to multiple comparison procedures, this book offers strategies for constructing the procedures and illustrates the framework for multiple hypotheses testing in general parametric models. It is suitable for readers with R experience but limited knowledge of multiple comparison procedures and vice versa. See Dr. Bretz discuss the book.
Book Synopsis Resampling-Based Multiple Testing by : Peter H. Westfall
Download or read book Resampling-Based Multiple Testing written by Peter H. Westfall and published by John Wiley & Sons. This book was released on 1993-01-12 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Book Synopsis Testing Statistical Hypotheses by : Erich L. Lehmann
Download or read book Testing Statistical Hypotheses written by Erich L. Lehmann and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
Book Synopsis Statistical Tolerance Regions by : Kalimuthu Krishnamoorthy
Download or read book Statistical Tolerance Regions written by Kalimuthu Krishnamoorthy and published by John Wiley & Sons. This book was released on 2009-05-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern and comprehensive treatment of tolerance intervals and regions The topic of tolerance intervals and tolerance regions has undergone significant growth during recent years, with applications arising in various areas such as quality control, industry, and environmental monitoring. Statistical Tolerance Regions presents the theoretical development of tolerance intervals and tolerance regions through computational algorithms and the illustration of numerous practical uses and examples. This is the first book of its kind to successfully balance theory and practice, providing a state-of-the-art treatment on tolerance intervals and tolerance regions. The book begins with the key definitions, concepts, and technical results that are essential for deriving tolerance intervals and tolerance regions. Subsequent chapters provide in-depth coverage of key topics including: Univariate normal distribution Non-normal distributions Univariate linear regression models Nonparametric tolerance intervals The one-way random model with balanced data The multivariate normal distribution The one-way random model with unbalanced data The multivariate linear regression model General mixed models Bayesian tolerance intervals A final chapter contains coverage of miscellaneous topics including tolerance limits for a ratio of normal random variables, sample size determination, reference limits and coverage intervals, tolerance intervals for binomial and Poisson distributions, and tolerance intervals based on censored samples. Theoretical explanations are accompanied by computational algorithms that can be easily replicated by readers, and each chapter contains exercise sets for reinforcement of the presented material. Detailed appendices provide additional data sets and extensive tables of univariate and multivariate tolerance factors. Statistical Tolerance Regions is an ideal book for courses on tolerance intervals at the graduate level. It is also a valuable reference and resource for applied statisticians, researchers, and practitioners in industry and pharmaceutical companies.
Book Synopsis Simultaneous Confidence Intervals and Multiple Tests for Multinomial Proportions by :
Download or read book Simultaneous Confidence Intervals and Multiple Tests for Multinomial Proportions written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Let us outline the contents of the chapters to follows.
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Simultaneous Confidence Intervals by : Maria Cristina Irene Peña Sison
Download or read book Simultaneous Confidence Intervals written by Maria Cristina Irene Peña Sison and published by . This book was released on 1995 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1978 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Comparisons Among Treatment Means in an Analysis of Variance by : Victor Chew
Download or read book Comparisons Among Treatment Means in an Analysis of Variance written by Victor Chew and published by . This book was released on 1977 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for Simultaneous Inclusion of Polynomial Zeros by : Miodrag Petkovic
Download or read book Iterative Methods for Simultaneous Inclusion of Polynomial Zeros written by Miodrag Petkovic and published by Springer. This book was released on 2006-11-14 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous approximation of polynomial zeros, where automatic procedure selection is desired. The book is both a text and a reference source for mathematicans, engineers, physicists and computer scientists who are interested in new developments and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis and programming.
Book Synopsis Multiple Testing and False Discovery Rate Control by : Shiyun Chen
Download or read book Multiple Testing and False Discovery Rate Control written by Shiyun Chen and published by . This book was released on 2019 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple testing, a situation where multiple hypothesis tests are performed simultaneously, is a core research topic in statistics that arises in almost every scientific field. When more hypotheses are tested, more errors are bound to occur. Controlling the false discovery rate (FDR) [BH95], which is the expected proportion of falsely rejected null hypotheses among all rejections, is an important challenge for making meaningful inferences. Throughout the dissertation, we analyze the asymptotic performance of several FDR-controlling procedures under different multiple testing settings. In Chapter 1, we study the famous Benjamini-Hochberg (BH) method [BH95] which often serves as benchmark among FDR-controlling procedures, and show that it is asymptotic optimal in a stylized setting. We then prove that a distribution-free FDR control method of Barber and Candès [FBC15], which only requires the (unknown) null distribution to be symmetric, can achieve the same asymptotic performance as the BH method, thus is also optimal. Chapter 2 proposes an interval-type procedure which identifies the longest interval with the estimated FDR under a given level and rejects the corresponding hypotheses with P-values lying inside the interval. Unlike the threshold approaches, this procedure scans over all intervals with the left point not necessary being zero. We show that this scan procedure provides strong control of the asymptotic false discovery rate. In addition, we investigate its asymptotic false non-discovery rate (FNR), deriving conditions under which it outperforms the BH procedure. In Chapter 3, we consider an online multiple testing problem where the hypotheses arrive sequentially in a stream, and investigate two procedures proposed by Javanmard and Montanari [JM15] which control FDR in an online manner. We quantify their asymptotic performance in the same location models as in Chapter 1 and compare their power with the (static) BH method. In Chapter 4, we propose a new class of powerful online testing procedures which incorporates the available contextual information, and prove that any rule in this class controls the online FDR under some standard assumptions. We also derive a practical algorithm that can make more empirical discoveries in an online fashion, compared to the state-of-the-art procedures.
Book Synopsis Analyzing Environmental Data by : Walter W. Piegorsch
Download or read book Analyzing Environmental Data written by Walter W. Piegorsch and published by John Wiley & Sons. This book was released on 2005-06-10 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Environmental statistics is a rapidly growing field, supported by advances in digital computing power, automated data collection systems, and interactive, linkable Internet software. Concerns over public and ecological health and the continuing need to support environmental policy-making and regulation have driven a concurrent explosion in environmental data analysis. This textbook is designed to address the need for trained professionals in this area. The book is based on a course which the authors have taught for many years, and prepares students for careers in environmental analysis centered on statistics and allied quantitative methods of data evaluation. The text extends beyond the introductory level, allowing students and environmental science practitioners to develop the expertise to design and perform sophisticated environmental data analyses. In particular, it: Provides a coherent introduction to intermediate and advanced methods for modeling and analyzing environmental data. Takes a data-oriented approach to describing the various methods. Illustrates the methods with real-world examples Features extensive exercises, enabling use as a course text. Includes examples of SAS computer code for implementation of the statistical methods. Connects to a Web site featuring solutions to exercises, extra computer code, and additional material. Serves as an overview of methods for analyzing environmental data, enabling use as a reference text for environmental science professionals. Graduate students of statistics studying environmental data analysis will find this invaluable as will practicing data analysts and environmental scientists including specialists in atmospheric science, biology and biomedicine, chemistry, ecology, environmental health, geography, and geology.
