Optimal Sequentially Planned Decision Procedures

This volume is concerned with statistical procedures where the data are collected in sequentially designed groups 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.

Zusammenfassung
Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner.

Inhalt
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 ofpolicies 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.