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.