We consider designs when interest is in estimating the optimal factor combination in a multiple quadratic regression setup, supposing that this factor combination belongs to a given set. By involving the concepts of admissibility and invariance of designs we substantially reduce the problem of calculating minimax designs. Exemplary, we give optimal designs for some setups on the ball and on the cube. © 1992.

N K MANDAL

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Minimax designs for estimating the optimum point in a quadratic response surface

Journal of Statistical Planning and Inference

In the analysis of experiments with mixtures, quadratic models have been widely used. The optimum designs for the estimation of optimum mixing proportions in a quadratic mixture model have been studied by Pal and Mandal [Optimum designs for optimum mixtures. Statist Probab Lett. 2006;76:1369–1379] and Mandal et al. [Optimum mixture designs: a pseudo-Bayesian approach. J Ind Soc Agric Stat. 2008;62(2):174–182; Optimum mixture designs under constraints on mixing components. Statist Appl. 2008;6(1&2) (New Series): 189–205], using a pseudo-Bayesian approach. In this paper, a similar approach has been employed to obtain the A-optimal designs for the estimation of optimum proportions in an additive quadratic mixture model, proposed by Darroch and Waller [Additivity and interaction in three-component experiments with mixture. Biometrika. 1985;72:153–163], when the number of components is 3, 4 and 5. It has been shown that the vertices of the simplex are necessarily the support points of the optimum design, and the other support points include barycentres of depth at most 2. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Statistics

A-optimal designs for optimum mixture in an additive quadratic mixture model

In this paper, we consider the estimation of the optimum factor combination in a response surface model. Assuming that the response function is quadratic concave and there is a linear cost constraint on the factor combination, we attempt to find the optimum design using the trace optimality criterion. As the criterion function involves the unknown parameters, we adopt a pseudo-Bayesian approach to resolve the problem. © 2009 Taylor & Francis.

Journal of Applied Statistics

Optimum designs for estimation of optimum point under cost constraint

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe [1958. Experiments with mixtures. Journal of Royal Statistical Society B 20, pp. 344-360; 1963. Simplex-centroid design for experiments with mixtures. Journal of Royal Statistical Society B 25, 235-263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal [2006. Optimum designs for optimum mixtures. Statistics and Probability Letters 76, 1369-1379] first attempted to find a solution to this problem using the trace criterion, assuming prior knowledge about the optimum mixing proportions. In this paper the minimax criterion has been employed to find a solution to the above problem. © 2007.

Statistics and Probability Letters

Minimax designs for optimum mixtures

In a mixture experiment the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffe (1958, 1963) first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. The problem of estimating the optimum proportion of mixture components is of great practical importance. Pal and Mandal (2006, 2007) attempted to find a solution to this problem by adopting a pseudo-Bayesian approach and using the trace criterion. Subsequently, Pal and Mandal (2008) solved the problem using minimax criterion. In this article, the deficiency criterion due to Chatterjee and Mandal (1981) has been used as a measure for comparing the performance of competing designs.

Communications in Statistics - Theory and Methods

Optimum mixture design using deficiency criterion

In a mixture experiment, the measured response is assumed to depend only on the relative proportion of ingredients or components present in the mixture. Scheffé [1958. Experiments with mixtures. J. Roy. Statist. Soc. B 20, 344-360; 1963. Simplex-centroid design for experiments with mixtures. J. Roy. Statist. Soc. B 25, 235-263] first systematically considered this problem and introduced different models and designs suitable in such situations. Optimum designs for the estimation of parameters of different mixture models are available in the literature. However, in a mixture experiment, often one is more interested in the optimum proportion of ingredients. In this paper, we try to find optimum designs for the estimation of optimum mixture combination on the assumption that the response function is quadratic concave over the simplex region. © 2006 Elsevier B.V. All rights reserved.

Journal	Journal of Statistical Planning and Inference
Publisher	-
ISSN	0378-3758