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Optimal allocation of bioassays in the case of parametrized covariance functions: an application to Lung’s retention of radioactive particles

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Abstract

In this paper, we investigate the effect of employing a parametrized covariance function in a regression experiment on corresponding optimum designs. We demonstrate these effects in the framework of a real example for measuring the lung’s retention of radioactive particles. Also, two different covariance functions are considered, and it is shown that this choice can play a crucial role.

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References

  • Abt M, Welch WJ (1998) Fisher information and maximum-likelihood estimation of covariance parameters in Gaussian stochastic processes. Can J Stat 26:127–137

    Article  MATH  MathSciNet  Google Scholar 

  • Adler RJ, Taylor JE (2005) Random fields and geometry. Birkhäuser, Boston

    Google Scholar 

  • Brimkulov UN, Krug GK, Savanov VL (1980) Numerical construction of exact experimental designs when the measurements are correlated. Zavodskaya Laboratoria (Ind Lab) 36:435–442 (In Russian)

    Google Scholar 

  • Cressie N (1993) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Hedayat AS, Zhong J, Nie L (2004) Optimal and efficient designs for 2-parameter nonlinear models. J Stat Plan Inference 124:205–217

    Article  MATH  MathSciNet  Google Scholar 

  • Hill PDH (1980) D-optimal designs for partially nonlinear regression models. Technometrics 22:275–276

    Article  MATH  MathSciNet  Google Scholar 

  • ICRP66:94 (1994) International commission on radiological protection, human respiratory tract model for radiological protection. Pergamon, Oxford (ICRP Publication, 66 edn)

    Google Scholar 

  • López-Fidalgo J, Rodríguez-Díaz JM, Sánchez G, Santos-Martín MT (2005) Optimal design for compartmental models with correlated observations. J Appl Stat 32(10):1075–1088

    Article  MATH  MathSciNet  Google Scholar 

  • Melas VB (1978) Optimal designs for exponential regression. Math Oper Stat Ser Stat 9(1):45–59

    MATH  MathSciNet  Google Scholar 

  • Moerbeek M (2005) Robustness properties of A-, D- and E-optimal designs for polynomial growth models with autocorrelated errors. Comput Stat Data Anal (48):765–778

  • Müller WG, Pázman A (2003) Measures for designs in experiments with correlated errors. Biometrika 90(2):765–778

    Article  MathSciNet  Google Scholar 

  • Müller WG, Stehlík M (2004) An example of D-optimal designs in the case of correlated errors. In: Antoch J (ed) Proceedings of COMPSTAT2004. Springer, Berlin, pp 1519–1526

    Google Scholar 

  • Näther W (1985) Effective observation of random fields. Teubner-Texte zur Mathematik, vol 72. Teubner, Leipzig

    MATH  Google Scholar 

  • Pázman A (2004) Correlated optimum design with parametrized covariance function: justification of the Fisher information matrix and of the method of virtual noise. Research report series Nr. 5, Department of Statistics and Mathematics, University of Economics and Business Administration, Vienna

  • Stehlík M (2004) Further aspects on an example of D-optimal designs in the case of correlated errors. Research report series Nr. 1, Department of Statistics and Mathematics, University of Economics and Business Administration, Vienna

  • Stehlík M (2005) Covariance related properties of D-optimal correlated designs. In: Ermakov SM, Melas VB, Pepelyshev AN (eds) Proceedings of the 5th St. Petersburg workshop on simulation. NII Chemistry St. Petersburg University, St. Petersburg, pp 645–652

    Google Scholar 

  • Uciński D, Atkinson AC (2004) Experimental design for time-dependent models with correlated observations. Stud Nonlinear Dyn Econom 8(2):1217–1217

    Google Scholar 

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Correspondence to Werner G. Müller.

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Stehlík, M., Rodríguez-Díaz, J.M., Müller, W.G. et al. Optimal allocation of bioassays in the case of parametrized covariance functions: an application to Lung’s retention of radioactive particles. TEST 17, 56–68 (2008). https://doi.org/10.1007/s11749-006-0022-x

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  • DOI: https://doi.org/10.1007/s11749-006-0022-x

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