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Optimal Sequentially Planned Decision Procedures (Lecture Notes in Statistics, 79) - Schmitz, Norbert
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Schmitz, Norbert:

Optimal Sequentially Planned Decision Procedures (Lecture Notes in Statistics, 79) - First edition

1992, ISBN: 9780387979083

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Optimal Sequentially Planned Decision Procedures - Norbert Schmitz
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Norbert Schmitz:

Optimal Sequentially Planned Decision Procedures - Paperback

ISBN: 9780387979083

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Optimal Sequentially Planned Decision Procedures. Lecture Notes in Statistics 79 - used book

1992

ISBN: 9780387979083

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Optimal Sequentially Planned Decision Procedures (Lecture Notes in Statistics) (v. 79) - Schmitz, Norbert; Duscha, G. [Assistant]; Lübbert, J. [Assistant]; Meyerthole, T. [Assistant];
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Schmitz, Norbert; Duscha, G. [Assistant]; Lübbert, J. [Assistant]; Meyerthole, T. [Assistant];:
Optimal Sequentially Planned Decision Procedures (Lecture Notes in Statistics) (v. 79) - Paperback

1992, ISBN: 0387979085

[EAN: 9780387979083], [PU: Springer], Interior clean, binding tight, moderate wear to covers., Books

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Optimal Sequentially Planned Decision Procedures - Norbert Schmitz
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Norbert Schmitz:
Optimal Sequentially Planned Decision Procedures - Paperback

1992, ISBN: 0387979085

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Optimal Sequentially Planned Decision Procedures
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ISBN:

0387979085


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.

Details of the book - Optimal Sequentially Planned Decision Procedures


EAN (ISBN-13): 9780387979083
ISBN (ISBN-10): 0387979085
Hardcover
Paperback
Publishing year: 1992
Publisher: Springer New York

Book in our database since 2007-05-17T20:51:08-04:00 (New York)
Detail page last modified on 2023-10-20T08:32:05-04:00 (New York)
ISBN/EAN: 0387979085

ISBN - alternate spelling:
0-387-97908-5, 978-0-387-97908-3
Alternate spelling and related search-keywords:
Book author: norbert schmitz, duscha, lübbert, norbert thomas, eke norbert, rise
Book title: optimal, procedures, decision

Information from Publisher

Author: Norbert Schmitz
Title: Lecture Notes in Statistics; Optimal Sequentially Planned Decision Procedures
Publisher: Springer; Springer US
207 Pages
Publishing year: 1992-10-28
New York; NY; US
Language: English
106,99 € (DE)
109,99 € (AT)
118,00 CHF (CH)
Available
XII, 207 p.

BC; Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik; Wahrscheinlichkeitsrechnung und Statistik; Verstehen; Hypothese; Power; Sequential Probability Ratio Test; probability; Probability Theory; Stochastik; EA

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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