The Annals of Statistics
- Ann. Statist.
- Volume 17, Number 3 (1989), 1087-1102.
Very Weak Expansions for Sequentially Designed Experiments: Linear Models
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.
Ann. Statist., Volume 17, Number 3 (1989), 1087-1102.
First available in Project Euclid: 12 April 2007
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Woodroofe, Michael. Very Weak Expansions for Sequentially Designed Experiments: Linear Models. Ann. Statist. 17 (1989), no. 3, 1087--1102. doi:10.1214/aos/1176347257. https://projecteuclid.org/euclid.aos/1176347257