Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. 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. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential…mehr
Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. 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. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]_) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.
Manfred Breithaupt ist Senior Planning Officer der Energie- und Transportabteilung der Deutschen Gesellschaft für Technische Zusammenarbeit (GTZ) GmbH in Eschborn. Horst Höfling führt seit über 20 Jahren als Diplom-Ingenieur der Elektrotechnik Energieprojekte für die GTZ. Lars Petzold ist Seniorberater der Kienbaum Development Services GmbH in Düsseldorf. Christine Philipp ist Diplom-Volkswirtin und Mitarbeiterin der Kienbaum Development Services GmbH in Düsseldorf. Dr. Norbert Schmitz ist Geschäftsleiter der Kienbaum Development Services GmbH in Düsseldorf. Dr. Rolf Sülzer ist Direktor des GTZ-Landesbüros Thailand in Bangkok.
Inhaltsangabe
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.
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.
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