Sequential Analysis and Optimal Design

Herman Chernoff9780898710069, 0898710065

An exploration of the interrelated fields of design of experiments and sequential analysis with emphasis on the nature of theoretical statistics and how this relates to the philosophy and practice of statistics.

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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