Experimental Design Theory Research Articles

Optimization of measurement schedules and sensor designs for linear dynamic systems

This paper presents new results on the problem of measurement scheduling, sensor location, and design for linear dynamic systems. Both time-invariant and time-varying systems are considered and different norms of the observability and information matrices are maximized with respect to the structural parameters of the system. A close connection is established between these problems and the Kiefer-Wolfowitz theory of experimental design for regression problems. Both randomized and nonrandomized designs are considered. It is shown that the optimal designs obey certain minmax properties that lead to rapidly convergent algorithms. The results are illustrated by an analytical and a numerical example.

Discussion on the Paper by Dr Atkinson and Professor Cox

Journal of the Royal Statistical Society: Series B (Methodological)Volume 36, Issue 3 p. 335-348 DiscussionFree Access Discussion on the Paper by Dr Atkinson and Professor Cox Correction(s) for this article Correction Volume 37Issue 2Journal of the Royal Statistical Society: Series B (Methodological) pages: 296-296 First Published online: December 5, 2018 First published: July 1974 https://doi.org/10.1111/j.2517-6161.1974.tb01011.xAboutPDF ToolsExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat References in the Discussion Andrews, D. F. (1972). Plots of high-dimensional data. Biometrics, 28, 125– 136. Atkinson, A. C. (1970). A method for discriminating between models. J. R. Statist. Soc. B, 32, 323– 353. Atkinson, A. C. (1975). Planning experiments for model testing and discrimination. Math. Operationsforsch. u. Statist., 6 (in press). Chambers, E. A. and Cox, D. R. (1967). Discrimination between alternative binary response models. Biometrika, 54, 573– 578. Chernoff, H. (1959). Sequential design of experiments. Ann. Math. Statist., 30, 755– 770. Chernoff, H. (1974). Approaches in sequential design of experiments. In A Survey of Statistical Design and Linear Models, ( J. N. Srivastava, ed.) Colorado State University. Cochran, W. G. (1973). Experiments for nonlinear functions. J. Amer. Statist. Ass., 68, 771– 781. Cox, D. R. (1962). Further results on tests of separate families of hypotheses. J. R. Statist. Soc. B, 24, 406– 424. Fedorov, V. V. (1971). Asymptotically optimal designs of experiments for discriminating two rival regression models. Theory Probab. Applic., 16, 561. Fedorov, V. V. (1973). Planning Optimum Experiments when there is some Information about Rival Models. Moscow: State University Press (in Russian). Karlin, S. (1959). Mathematical Methods and Theory in Games, Programming and Economics, Vol. II. Addison Wesley. Lindley, D. V. and Smith, A. F. M. (1972). Bayes estimates for the linear model. J. R. Statist. Soc. B, 34, 1– 41. Pazman, A. (1974). A convergence theorem in the theory of D-optimum experimental designs. Ann. Statist., 2, 216– 218. Whittle, P. (1965). Some general results in sequential design (with discussion). J. R. Statist. Soc. B, 27, 371– 394. Volume36, Issue3July 1974Pages 335-348 This article also appears in:Discussion Papers ReferencesRelatedInformation

Special considerations in the use of multifactorial experimental design theory for metrological tests

Special considerations in the use of multifactorial experimental design theory for metrological tests

Some General Points in the Theory of Optimal Experimental Design

Summary This paper is an expansion of comments made by the author in the discussion following the reading of papers by Laycock (1972) and Wynn (1972). Section 2 presents a direct proof and interpretation of the equivalence theorem for the general case of a concave criterion function. This has implications for iterative algorithms of the type suggested by Wynn, as indicated in Section 3. Section 4 is concerned with a characterization of D,-optimality as a criterion which preserves ranking of designs under certain transformations of the problem. Section 5 discusses quasi-linear representations of the criterion for c-optimality.

Choice of Response Functional Form in Designing Subsidy Experiments

EXPERIMENT DESIGN THEORY for regression analysis is becoming important in econometric work, most notably in the context of negative income tax [1] and other subsidy experiments (such as housing and health subsidy experiments being planned). The usual regression design model requires the experimenter to specify the functional form of the behavioral equation under investigation. An apparent difficulty is that the experimenter does not know the true functional form. This paper suggests new procedures for handling the difficulty. The procedures were stimulated by work in planning the New Jersey negative tax experiment. To the planners of the New Jersey experiment, the relevant statistical design literature was not applicable, cookbook fashion, because the practical design guidelines were constructed for simpler situations. However, by combining ingredients from the statistical literature, the New Jersey experimenters were able to define a well-behaved mathematical programming model whose solution would tailor a design to their situation [3]. (The references [2 and 4] provide a useful entry to the relevant statistical literature.) The new procedures suggested here build on the New Jersey design model, which is reviewed in Section 2. Though the exposition runs in terms of subsidy experiments, the material is more generally applicable.

On maximal (k,t)-sets

This investigation was originally motivated by the problem of determining the maximum number of points in finiten-dimensional projective spacePG(n, s) based on the Galois fieldGF(s) of orders=ph (wherep andh are positive integers andp is the prime characteristic of the field), such that not of these chosen points are linearly dependent. A set ofk distinct points inPG(n, s), not linearly dependent, is called a (k, t)-set fork1>k. The maximum value ofk is denoted bymt(n+1, s). The purpose of this paper is to find new upper bounds for some values ofn, s andt. These bounds are of importance in the experimental design and information theory problems.

A method of constructin g balanced incomplete block desi gns

Dr Eric-Roy Muller was a research student in the Department of Statistics, University of Aberdeen from 1959 to 1962. A scientist of great promise, he received the degree of Ph.D. in June 1962 for his thesis ‘On Confounding of Asymmetrical Factorial Designs’. Shortly afterwards, he returned to his position in the Department of Statistics, University of Natal. In January 1963, he and his wife were killed tragically when their car was hit by a train at a level crossing. Roy Muller's thesis included critical discussion of the problems that arise in confounding factorial arrangements, in such a way as to conserve information on the most important contrasts, when the combinations of factor levels and block size present difficulties not encountered in the classical factorial designs. His pseudo-factors and related devices provide new methods of construction and some new designs. In the belief that this work is of value to the general theory of experimental design, and as a tribute to our friend and fellow statistician, my colleagues and I hope to condense parts of the thesis for publication. This first paper, though a digression from the main theme, develops a method that is to be used later.

Finney, D. J.: An introduction to the theory of experimental design. The University of Chicago Press, Chicago 1960; 223 S., $ 7,—

Biometrische ZeitschriftVolume 4, Issue 1 p. 69-70 Buchbesprechung Finney, D. J.: An introduction to the theory of experimental design. The University of Chicago Press, Chicago 1960; 223 S., $ 7,— G. Enderlein, G. EnderleinSearch for more papers by this author G. Enderlein, G. EnderleinSearch for more papers by this author First published: 1962 https://doi.org/10.1002/bimj.19620040112AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume4, Issue11962Pages 69-70 RelatedInformation