Sequential Analysis and Optimal Design [SIAM ed.] 9780898710069, 0898710065
An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature o
221 107 1MB
English Pages 131 Year 1987
Table of contents :
Sequential Analysis and Optimal Design......Page 1
Contents......Page 7
Preface......Page 9
Sequential Analysis and Optimal Design......Page 11
Generalities about the conventional theory of design of experiments.......Page 13
Optimal sample size.......Page 15
Preliminaries on regression.......Page 18
Design for linear regression: Elfving's method.......Page 23
Maximum-likelihood estimation.......Page 26
Locally optimal designs for estimation.......Page 33
More design in regression experiments.......Page 41
Testing hypotheses.......Page 47
Optimal sample size in testing.......Page 65
Sequential probability-ratio......Page 67
Optimality of sequential probability-ratio test.......Page 73
Motivation for an approach to sequential design of experiments in testing hypotheses.......Page 76
Asymptotic optimality of Procedure A in sequential design.......Page 80
Extensions and open questions in sequential design.......Page 82
The problem of adjacent hypotheses.......Page 85
Testing for the sign of a normal mean: no indifference zone.......Page 94
Bandit problems.......Page 112
Sequential estimation of a normal mean.......Page 118
Sequential estimation of the common mean of two normal populations.......Page 121
Conclusion.......Page 127
Sequential Analysis and Optimal Design......Page 1
Contents......Page 7
Preface......Page 9
Sequential Analysis and Optimal Design......Page 11
Generalities about the conventional theory of design of experiments.......Page 13
Optimal sample size.......Page 15
Preliminaries on regression.......Page 18
Design for linear regression: Elfving's method.......Page 23
Maximum-likelihood estimation.......Page 26
Locally optimal designs for estimation.......Page 33
More design in regression experiments.......Page 41
Testing hypotheses.......Page 47
Optimal sample size in testing.......Page 65
Sequential probability-ratio......Page 67
Optimality of sequential probability-ratio test.......Page 73
Motivation for an approach to sequential design of experiments in testing hypotheses.......Page 76
Asymptotic optimality of Procedure A in sequential design.......Page 80
Extensions and open questions in sequential design.......Page 82
The problem of adjacent hypotheses.......Page 85
Testing for the sign of a normal mean: no indifference zone.......Page 94
Bandit problems.......Page 112
Sequential estimation of a normal mean.......Page 118
Sequential estimation of the common mean of two normal populations.......Page 121
Conclusion.......Page 127
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