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Observed Confidence Levels

Theory and Application

By Alan M. Polansky

Chapman and Hall/CRC – 2007 – 288 pages

Purchasing Options:

  • Add to CartHardback: $104.95
    978-1-58488-802-4
    October 26th 2007

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, Statistical Computing