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Very Weak Expansions for Sequentially Designed Experiments: Linear Models
The Annals of Statistics
Vol. 17, No. 3 (Sep., 1989), pp. 1087-1102
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2241711
Page Count: 16
You can always find the topics here!Topics: Approximation, Experiment design, Martingales, Simulations, Stopping distances, Maximum likelihood estimators, Density, Statism, Linear models, Sampling distributions
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In sequentially designed experiments with linear models, each design variable may depend on previous responses. The use of such sequential designs does not affect the likelihood function or the functional form of the maximum likelihood estimator, but it may affect sampling distributions. In this paper, asymptotic expansions for sampling distributions are obtained. The expansions are very weak ones in which a confidence curve (a function of the unknown parameters) is replaced by a confidence functional defined on a class of prior distributions. The proofs use a version of Stein's identity.
The Annals of Statistics © 1989 Institute of Mathematical Statistics