Book ChapterDOI
Optimum Experimental Designs
TLDR
In this article, the authors discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc.Abstract:
After some introductory remarks, we discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc. In section 3 we discuss complete classes of designs, while in section 4 we consider methods for verifying that designs satisfy certain specific optimality criteria, or for computing designs which satisfy such criteria. Some of the results are new, while part of the paper reviews pertinent results of the author and others.read more
Citations
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Journal ArticleDOI
The Future of Data Analysis
TL;DR: For a long time I have thought I was a statistician, interested in inferences from the particular to the general as mentioned in this paper. But as I have watched mathematical statistics evolve, I have had cause to wonder and to doubt.
Journal ArticleDOI
Environmental impact assessment: "pseudoreplication" in time?'
TL;DR: An appropriate sampling scheme designed to detect the effect of the discharge upon this underlying mean of the underlying probabilistic "process" that produces the abundance, rather than the actual abundance itself is described.
Journal Article
Covariate Shift Adaptation by Importance Weighted Cross Validation
TL;DR: This paper proposes a new method called importance weighted cross validation (IWCV), for which its unbiasedness even under the covariate shift is proved, and the IWCV procedure is the only one that can be applied for unbiased classification under covariates.
Journal ArticleDOI
General Equivalence Theory for Optimum Designs (Approximate Theory)
TL;DR: For general optimality criteria, this article obtained criteria equivalent to $\Phi$-optimality under various conditions on ''Phi'' and showed that such equivalent criteria are useful for analytic or machine computation of ''phi''-optimum designs.
Journal ArticleDOI
Optimal input signals for parameter estimation in dynamic systems--Survey and new results
TL;DR: This paper surveys the field of optimal input design for parameter estimation as it has developed over the last two decades, with a derivation of the Fisher information matrix for multiinput multioutput systems with process noise.
References
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Journal ArticleDOI
A Stochastic Approximation Method
Herbert Robbins,Sutton Monro +1 more
TL;DR: In this article, a method for making successive experiments at levels x1, x2, ··· in such a way that xn will tend to θ in probability is presented.
Book ChapterDOI
On the Experimental Attainment of Optimum Conditions
George E. P. Box,K. B. Wilson +1 more
TL;DR: The work described in this article is the result of a study extending over the past few years by a chemist and a statistician, which has come about mainly in answer to problems of determining optimum conditions in chemical investigations, but they believe that the methods will be of value in other fields where experimentation is sequential and the error fairly small.
Journal ArticleDOI
The design of optimum multifactorial experiments
R. L. Plackett,J. P. Burman +1 more
Journal ArticleDOI
Stochastic Estimation of the Maximum of a Regression Function
J. Kiefer,Jacob Wolfowitz +1 more
TL;DR: In this article, the authors give a scheme whereby, starting from an arbitrary point, one obtains successively $x_2, x_3, \cdots$ such that the regression function converges to the unknown point in probability as n \rightarrow \infty.
Journal ArticleDOI
Some aspects of the sequential design of experiments
TL;DR: The authors proposed a theory of sequential design of experiments, in which the size and composition of the samples are not fixed in advance but are functions of the observations themselves, which is a major advance.