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Optimal designs for some stochastic processes whose covariance is a function of the mean

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Abstract

This paper considers optimal experimental designs for models with correlated observations through a covariance function depending on the magnitude of the responses. This suggests the use of stochastic processes whose covariance structure is a function of the mean. Covariance functions must be positive definite. This fact is nontrivial in this context and constitutes one of the challenges of the present paper. We show that there exists a huge class of functions that, composed with the mean of the process in some way, preserves positive definiteness and can be used for the purposes of modeling and computing optimal designs in more realistic situations. We offer some examples for an easy construction of such covariances and then study the problem of locally D-optimal designs through an illustrative example as well as a real radiation retention model in the human body.

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Acknowledgements

Jesús López-Fidalgo and Mariano Amo-Salas are supported by Ministerio de Economía y Competitividad and Fondos FEDER MTM2010-20774-C03-01 and Junta de Comunidades de Castilla la Mancha PEII10-0291-1850.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Medicine, University of Castilla-La Mancha, Camino de Moledores s/n, 13071, Ciudad Real, Spain

    Mariano Amo-Salas

  2. Department of Mathematics, E.T.S.I. Industriales, University of Castilla-La Mancha, Avd. Camino José Cela s/n, 13071, Ciudad Real, Spain

    Jesús López-Fidalgo

  3. Departamento de Estadística, Universidad de Valparaiso, Gran Bretana 1111, Playa Ancha, 2360102, Valparaiso, Chile

    Emilio Porcu

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  1. Mariano Amo-Salas
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  2. Jesús López-Fidalgo
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  3. Emilio Porcu
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Correspondence to Mariano Amo-Salas.

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Amo-Salas, M., López-Fidalgo, J. & Porcu, E. Optimal designs for some stochastic processes whose covariance is a function of the mean. TEST 22, 159–181 (2013). https://doi.org/10.1007/s11749-012-0311-5

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  • DOI: https://doi.org/10.1007/s11749-012-0311-5

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