Observed Confidence Levels
Theory and Application
By Alan M. Polansky
Published October 26th 2007 by Chapman and Hall/CRC – 288 pages
Description
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.
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
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
Name: Observed Confidence Levels: Theory and Application (Hardback) – Chapman and Hall/CRC
Description: By Alan M. Polansky. 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...
Categories: Statistical Theory & Methods, Statistics for the Biological Sciences, Statistics & Computing
