Observed Confidence Levels

Observed Confidence Levels: Theory and Application

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Features

  • Compares the use of observed confidence levels with other statistical methodologies such as multiple comparisons and posterior probabilities
  • Includes many practical examples from the fields of engineering, biology, and medicine as well as exercises at the end of each chapter
  • Discusses how observed confidence levels can be computed using the R statistical computing environment
  • Offers a website with many of the data sets and R code used in the book as well as links to relevant references and news about current applications of observed confidence levels
  • Summary

    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.

    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

    Editorial Reviews

    … 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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