Observed Confidence Levels

Observed Confidence Levels : Theory and Application

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Illustrating a simple, novel method for solving an array of statistical problems, Observed Confidence Levels: Theory and Application describes the basic development of observed confidence levels, a methodology that can be applied to a variety of common multiple testing problems in statistical inference. It focuses on the modern nonparametric framework of bootstrap-based estimates, allowing for substantial theoretical development and for relatively simple solutions to numerous interesting problems. After an introduction, the book develops the theory and application of observed confidence levels for general scalar parameters, vector parameters, and linear models. It then examines nonparametric problems often associated with smoothing methods, including nonparametric density estimation and regression. The author also describes applications in generalized linear models, classical nonparametric statistics, multivariate analysis, and survival analysis as well as compares the method of observed confidence levels to hypothesis testing, multiple comparisons, and Bayesian posterior probabilities. In addition, the appendix presents some background material on the asymptotic expansion theory used in the book. Helping you choose the most reliable method for a variety of problems, this book shows how observed confidence levels provide useful information on the relative truth of hypotheses in multiple testing problems.
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Product details

  • Electronic book text | 288 pages
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 50 Illustrations, black and white
  • 1584888032
  • 9781584888031

Table of contents

Preface Introduction Introduction The Problem of Regions Some Example Applications About This Book Single Parameter Problems Introduction The General Case Smooth Function Model Asymptotic Comparisons Empirical Comparisons Examples Computation Using R Exercises Multiple Parameter Problems Introduction Smooth Function Model Asymptotic Accuracy Empirical Comparisons Examples Computation Using R Exercises Linear Models and Regression Introduction Statistical Framework Asymptotic Accuracy Empirical Comparisons Examples Further Issues in Linear Regression Computation Using R Exercises Nonparametric Smoothing Problems Introduction Nonparametric Density Estimation Density Estimation Examples Solving Density Estimation Problems Using R Nonparametric Regression Nonparametric Regression Examples Solving Nonparametric Regression Problems Using R Exercises Further Applications Classical Nonparametric Methods Generalized Linear Models Multivariate Analysis Survival Analysis Exercises Connections and Comparisons Introduction Statistical Hypothesis Testing Multiple Comparisons Attained Confidence Levels Bayesian Confidence Levels Exercises Appendix: Review of Asymptotic Statistics Taylor's Theorem Modes of Convergence Central Limit Theorem Convergence Rates Exercises References INDEX
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Review quote

... The text is at a Ph.D. level because of the asymptotic theory, but many of the ideas are simple and may be of great use. The text is useful for researchers who want to learn about observed confidence levels, and the topic of observed confidence levels would be a useful addition to a course on resampling methods such as the bootstrap. ... The website (www.math.niu.edu/~polansky/oclbook/) contains R functions and data sets.-Technometrics, May 2009, Vol. 51, No. 2
...The breadth of real examples that the author provides certainly demonstrates that this is a class of techniques worth considering.-International Statistical Review (2009), 77, 2

...In summary, the book was written with the objectives of educating the reader on the mechanics, general theory, practical implementation, and potential uses of observed confidence as a new approach to multiple testing. In my opinion the book delivers on these. Observed confidence is laid out, but not oversold, which I also appreciated ... I was impressed by both the text and the testing method.-Daniel J. Nordman, Iowa State University, Journal of the American Statistical Association, June 2009, Vol. 104, No. 486
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