Sequential Analysis and Optimal Design

Abstract

Preliminaries on probability Generalities about the conventional theory of design of experiments Optimal sample size Preliminaries on regression Design for linear regression: Elfving's method Maximum-likelihood estimation Locally optimal designs for estimation More design in regression experiments Testing hypotheses Optimal sample size in testing Sequential probability-ratio test Optimality of sequential probability-ratio test Motivation for an approach to sequential design of experiments in testing hypotheses Asymptotic optimality of procedure A in sequential design Extensions and open questions in sequential design The problem of adjacent hypotheses Testing for the sign of a normal mean: no indifference zone Bandit problems Sequential estimation of a normal mean sequential estimation of the common mean of two normal populations.

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