UID:
almahu_9947362834502882
Umfang:
XII, 207 p.
,
online resource.
ISBN:
9781461227366
Serie:
Lecture Notes in Statistics, 79
Inhalt:
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.
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9780387979083
Sprache:
Englisch
DOI:
10.1007/978-1-4612-2736-6
URL:
http://dx.doi.org/10.1007/978-1-4612-2736-6
Bookmarklink
