Mukhopadhyay N., De Silva B.M. Sequential methods and their applications

2009, Boca Raton: Chapman and Hall/CRC, 499 p.
ISBN10: 158488102X.
ISBN13: 978-1584881025.
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.Objectives, Coverage, and Hopes.Back to the Origin.
Recent Upturn and Positive Feelings.
The Objectives.
The Coverage.
Aims and Scope.
Final Thoughts.
Why Sequential?Tests of Hypotheses.
Estimation Problems.
Selection and Ranking Problems.
Computer Programs.
Sequential Probability Ratio Test.Termination and Determination of A and B.
ASN Function and OC Function.
Examples and Implementation.
Auxiliary Results.
Sequential Tests for Composite Hypotheses.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.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.Fixed-Width Confidence Intervals.
Bounded Risk Point Estimation.
Minimum Risk Point Estimation.
Some Selected Derivations.
Location Estimation: Negative Exponential Distribution.Fixed-Width Confidence Intervals.
Minimum Risk Point Estimation.
Selected Derivations.
Point Estimation of the Mean of an Exponential Population.Minimum Risk Estimation.
Bounded Risk Estimation.
Data Analyses and Conclusions.
Other Selected Multistage Procedures.
Some Selected Derivations.
Fixed-Width Intervals from MLEs.General Sequential Approach.
General Accelerated Sequential Approach.
Examples.
Data Analyses and Conclusions.
Some Selected Derivations.
Distribution-Free Methods in Estimation.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.Fixed-Size Confidence Region: Σ = σ2H.
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.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.Fixed-Width Confidence Intervals.
Minimum Risk Point Estimation.
Other Selected Multistage Procedures.
Some Selected Derivations.
Selecting the Best Normal Population.Indifference Zone Formulation.
Two-Stage Procedure.
Sequential Procedure.
Data Analyses and Conclusions.
Other Selected Multistage Procedures.
Some Selected Derivations.
Sequential Bayesian Estimation.Selected Fixed Sample Size Concepts.
Elementary Sequential Concepts.
Data Analysis.
Selected Applications.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.Big O(.) and Little o(.).
Some Probabilistic Notions and Results.
A Glimpse at Nonlinear Renewal Theory.
Abbreviations and Notation.
Statistical Tables.