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

Author

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  • Mariano Amo-Salas
  • Jesús López-Fidalgo
  • Emilio Porcu

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. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Mariano Amo-Salas & Jesús López-Fidalgo & Emilio Porcu, 2013. "Optimal designs for some stochastic processes whose covariance is a function of the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 159-181, March.
    • Handle: RePEc:spr:testjl:v:22:y:2013:i:1:p:159-181
    DOI: 10.1007/s11749-012-0311-5
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    References listed on IDEAS

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    1. Holger Dette & Weng Kee Wong, 1999. "Optimal Designs When the Variance Is A Function of the Mean," Biometrics, The International Biometric Society, vol. 55(3), pages 925-929, September.
    2. Ucinski Dariusz & Atkinson Anthony C., 2004. "Experimental Design for Time-Dependent Models with Correlated Observations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-16, May.
    3. Angelis, L. & Bora-Senta, E. & Moyssiadis, C., 2001. "Optimal exact experimental designs with correlated errors through a simulated annealing algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 37(3), pages 275-296, September.
    4. J. López-Fidalgo & R. Martín-Martín & M. Stehlík, 2008. "Marginally restricted D-optimal designs for correlated observations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(6), pages 617-632.
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    Cited by:

    1. Víctor Casero-Alonso & Jesús López-Fidalgo, 2015. "Optimal designs subject to cost constraints in simultaneous equations models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 701-713, December.
    2. Santiago Campos-Barreiro & Jesús López-Fidalgo, 2015. "D-optimal experimental designs for a growth model applied to a Holstein-Friesian dairy farm," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 491-505, September.

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