Mukhopadhyay / de Silva Sequential Methods and Their Applications

1. Auflage 2008
ISBN: 978-1-4200-1002-2
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 504 Seiten

Interactively Run Simulations and Experiment with Real or Simulated Data to Make Sequential Analysis Come Alive
Taking an accessible, nonmathematical approach to this field, Sequential Methods and Their Applications illustrates the efficiency of sequential methodologies when dealing with contemporary statistical challenges in many areas.
The book first explores fixed sample size, sequential probability ratio, and nonparametric tests. It then presents numerous multistage estimation methods for fixed-width confidence interval as well as minimum and bounded risk problems. The book also describes multistage fixed-size confidence region methodologies, selection methodologies, and Bayesian estimation. Through diverse applications, each chapter provides valuable approaches for performing statistical experiments and facilitating real data analysis.
Functional in a variety of statistical problems, the authors’ interactive computer programs show how the methodologies discussed can be implemented in data analysis. Each chapter offers examples of input, output, and their interpretations. Available online, the programs provide the option to save some parts of an output so readers can revisit computer-generated data for further examination with exploratory data analysis.

Through this book and its computer programs, readers will better understand the methods of sequential analysis and be able to use them in real-world settings.

Zielgruppe

Upper-level undergraduate and graduate statistics students, teachers, researchers, and professionals in statistics

Autoren/Hrsg.

Mukhopadhyay, Nitis

de Silva, Basil M.

Fachgebiete

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

Inhaltsverzeichnis

Preface

Objectives, Coverage, and Hopes
Introduction
Back to the Origin
Recent Upturn and Positive Feelings
The Objectives
The Coverage
Aims and Scope
Final Thoughts
Why Sequential?
Introduction
Tests of Hypotheses
Estimation Problems
Selection and Ranking Problems
Computer Programs
Sequential Probability Ratio Test
Introduction
Termination and Determination of A and B
ASN Function and OC Function
Examples and Implementation
Auxiliary Results
Sequential Tests for Composite Hypotheses
Introduction
Test for the Variance
Test for the Mean
Test for the Correlation Coefficient
Test for the Gamma Shape Parameter
Two-Sample Problem: Comparing the Means
Auxiliary Results
Sequential Nonparametric Tests
Introduction
A Test for the Mean: Known Variance
A Test for the Mean: Unknown Variance
A Test for the Percentile
A Sign Test
Data Analyses and Conclusions
Estimation of the Mean of a Normal Population
Introduction
Fixed-Width Confidence Intervals
Bounded Risk Point Estimation
Minimum Risk Point Estimation
Some Selected Derivations
Location Estimation: Negative Exponential Distribution
Introduction
Fixed-Width Confidence Intervals
Minimum Risk Point Estimation
Selected Derivations
Point Estimation of the Mean of an Exponential Population
Introduction
Minimum Risk Estimation
Bounded Risk Estimation
Data Analyses and Conclusions
Other Selected Multistage Procedures
Some Selected Derivations
Fixed-Width Intervals from MLEs
Introduction
General Sequential Approach
General Accelerated Sequential Approach
Examples
Data Analyses and Conclusions
Some Selected Derivations
Distribution-Free Methods in Estimation
Introduction
Fixed-Width Confidence Intervals for the Mean
Minimum Risk Point Estimation for the Mean
Bounded Length Confidence Interval for the Median
Data Analyses and Conclusions
Other Selected Multistage Procedures
Some Selected Derivations
Multivariate Normal Mean Vector Estimation
Introduction
Fixed-Size Confidence Region: S = s2H
Fixed-Size Confidence Region: Unknown Dispersion Matrix
Minimum Risk Point Estimation: Unknown Dispersion Matrix
Data Analyses and Conclusions
Other Selected Multistage Procedures
Some Selected Derivations
Estimation in a Linear Model
Introduction
Fixed-Size Confidence Region
Minimum Risk Point Estimation
Data Analyses and Conclusions
Other Selected Multistage Procedures
Some Selected Derivations
Estimating the Difference of Two Normal Means
Introduction
Fixed-Width Confidence Intervals
Minimum Risk Point Estimation
Other Selected Multistage Procedures
Some Selected Derivations
Selecting the Best Normal Population
Introduction
Indifference Zone Formulation
Two-Stage Procedure
Sequential Procedure
Data Analyses and Conclusions
Other Selected Multistage Procedures
Some Selected Derivations
Sequential Bayesian Estimation
Introduction
Selected Fixed Sample Size Concepts
Elementary Sequential Concepts
Data Analysis
Selected Applications
Introduction
Clinical Trials
Integrated Pest Management
Experimental Psychology: Cognition of Distance
A Problem from Horticulture
Other Contemporary Areas of Applications
Appendix: Selected Reviews, Tables, and Other Items
Introduction
Big O(.) and Little o(.)
Some Probabilistic Notions and Results
A Glimpse at Nonlinear Renewal Theory
Abbreviations and Notation
Statistical Tables
References
Index
Exercises appear at the end of each chapter.