Norbert Schmitz

Optimal Sequentially Planned Decision Procedures

Mitarbeit: Duscha, G.; Lübbert, J.; Meyerthole, T.

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Lecture Notes in Statistics .79
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-97908-3
• 1992.
• Seitenzahl: 228
• Erscheinungstermin: 28. Oktober 1992
• Englisch
• Abmessung: 235mm x 155mm x 13mm
• Gewicht: 285g
• ISBN-13: 9780387979083
• ISBN-10: 0387979085
• Artikelnr.: 24510987

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.