Overview

This volume is concerned with statistical procedures where the data are collected in sequentially designed groups. The basic premise here is that the expected total sample size is not always the appropriate criterion for evaluating statistical procedures, especially for nonlinear sampling costs (e.g. additive fixed costs) and in clinical trials. In fact, this criterion seems to have been a hindrance to the practical use of Wald's sequential probability ratio test (SPRT) despite its well-known optimum properties. This volume systematically develops decision procedures which retain the possibility of early stopping and remove some of the disadvantages of one-at-a-time sampling. In particular, for generalizations of the SPRT algorithms, methods for computing characteristics (such as operating characteristics or power functions, expected sampling costs, etc.) are developed and implemented. The procedures turn out to be optimal in a Bayesian sense as well as for problems with side conditions (e.g. specified bounds on error probabilities or expected sampling costs). A theory of optimal sampling is developed in order to prove the various properties of the procedures.

Full Product Details

Author:   G. Duscha ,  Norbert Schmitz ,  J. Lübbert ,  T. Meyerthole
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Volume:   79
Dimensions:   Width: 15.50cm , Height: 1.20cm , Length: 23.50cm
Weight:   0.353kg
ISBN:  

9780387979083

ISBN 10:   0387979085
Pages:   207
Publication Date:   28 October 1992
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

I. Introduction.- 1 Sequential statistical procedures.- 2 Objectives of sequential analysis.- 3 Historical remarks on the development of sequential analysis.- 4 Examples of sequential procedures; purely sequential statistical decision procedures.- 5 Objections to purely sequential statistical decision procedures.- 6 Sequentially planned statistical procedures.- II. Optimal sequential sampling plans.- 1 Problems of optimal sampling.- 2 Optimal sampling plans for finite horizon.- 3 Existence of optimal sampling plans for general A.- 4 Optimal sampling plans for the Markov case.- III. Sequentially planned tests; sequentially planned probability ratio tests.- 1 Notation.- 2 The iid case.- 3 Sequentially planned probability ratio tests.- 4 Algorithms for computing the OC- and ASC-function of SPPRT's in the iid case.- 5 Remarks on the implementation of the algorithms; Examples.- 6 Remarks on the comparison of the methods and on convergence-improvements for the BF-/EV- method.- IV. Bayes-optimal sequentially planned decision procedures.- 1 Introduction.- 2 Bayes-procedures.- 3 A posteriori-distributions.- 4 Bayes-optimal sampling plans; Markov case.- V. Optimal sequentially planned tests under side conditions.- 1 Decision problems with side conditions.- 2 Characterizations of optimal sequentially planned decision procedures.- 3 Sequentially planned tests for simple hypotheses in the iid case.- 4 The modified Kiefer-Weiss problem in the iid case.- 5 Locally optimal sequentially planned tests in the dominated iid case.- 6 Remarks on the monotonicity of the power functions of SPPRT's and GSPPRT's.- Appendix A: Mathematical models for sequentially planned sampling procedures.- A.1 The concept of policies by Mandelbaum and Vanderbei.- A.2 The concept of tactics by Krengel and Sucheston.- A.3 The concept of decision functions by Washburn and Willsky.- A.4 The concept of stopped decision models by Rieder.- Appendix B: Implementation of the algorithms EV, BF and ILE; Diophantine Approximation.- B.1 Listing of the modules.- B.2 Diophantine approximation.- Appendix C: References, Bibliography.

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