Polansky Observed Confidence Levels

Theory and Application
Erscheinungsjahr 2007
ISBN: 978-1-58488-803-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 288 Seiten

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.

Zielgruppe

Researchers and students of biostatistics and statistics.

Autoren/Hrsg.

Polansky, Alan M.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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