Filling and D-optimal Designs for the Correlated Generalized Exponential Model

  1. Rodríguez-Díaz, Juan M. 1
  2. Santos-Martín, Teresa 1
  3. Stehlík, Milan 2
  4. Waldl, Helmut 2
  1. 1 Universidad de Salamanca
    info

    Universidad de Salamanca

    Salamanca, España

    ROR https://ror.org/02f40zc51

  2. 2 Johannes Kepler University of Linz
    info

    Johannes Kepler University of Linz

    Linz, Austria

    ROR https://ror.org/052r2xn60

Buch:
Contributions to Statistics

ISSN: 1431-1968

ISBN: 9783790824094,  9783790824100

Datum der Publikation: 2010

Seiten: 173-180

Art: Buch-Kapitel

DOI: 10.1007/978-3-7908-2410-0_23 GOOGLE SCHOLAR lock_openOpen Access editor

Zusammenfassung

The aim of this paper is to provide guidelines for efficient statistical es- timation of the parameters of the modified Arrhenius model for chemical kinetics. We study D-optimal and filling designs for this model, assuming correlated obser- vations and exponential covariance with or without nugget effect. We consider both equidistant and exact designs for small samples, and study the behaviour of different types of filling designs when a greater number of observations is preferred.

Bibliographische Referenzen

  • Abt, M. and W. Welch (1998). Fisher information and maximum-likelihood estimation of covariance parameters in gaussian stochastic processes. Canadian Journal of Statistics 26, 127–137.
  • Dette, H. and S. Sperlich (1994). A note on Bayesian D-optimal designs for a generalizarion of the exponential growth model. South African Statistical Journal 28, 103–117.
  • Gierczak, T., R. Talukdar, S. Herndon, G. Vaghjiani, and A. Ravishankara (1997). Rate coefficients for the reactions of hydroxyl radical with methane and deuterated methanes. Journal of Physical Chemistry A 101, 3125–3134.
  • Hill, P. (1980). D-optimal designs for partially nonlinear regression models. Technometrics 22, 275–276.
  • International Union of Pure and Applied Chemistry (IUPAC) (2008). Transition state theory. Technical report, http://goldbook.iupac.org/T06470.html .
  • Jet Propulsion Laboratory (2006). Chemical kinetics and photochemical data for use in atmospheric studies, NASA panel for data evaluation. Technical report, California Institute of Technology, Pasadena, California.
  • KiseǏák, J. and M. Stehlík (2008). Equidistant D -optimal designs for parameters of Ornstein-Uhlenbeck processes. Statistics and Probability Letters 78, 1388–1396.
  • Laidler, K. J. (1984). The development of the Arrhenius equation. Journal of Chemical Education 61, 494–498.
  • López-Fidalgo, J. and W. Wong (2002). Design issues for the Michaelis-Menten model. Journal of Theoretical Biology 215, 1–11.
  • Müller, W. and M. Stehlík (2009). Issues in the optimal design of computer simulation experiments. Applied Stochastic Models in Business and Industry 25, 163–177.
  • Müller, W. and M. Stehlík (2010). Compound optimal spatial designs. Environmetrics DOI: 10.1002/env.1009.
  • Pázman, A. (2007). Criteria for optimal design for small-sample experiments with correlated observations. Kybernetika 43, 453–462.
  • Rodríguez-Aragón, L. and J. López-Fidalgo (2005). Optimal designs for the arrhenius equation. Chemometrics & Intelligent Laboratory Systems 77, 131–138.
  • Rodríguez-Díaz, J. and M. Santos-Martín (2009). Study of the best designs for modifications of the arrhenius equation. Chemometrics & Intelligent Laboratory Systems 95, 199–208.
  • Rodríguez-Díaz, J., T. Santos-Martín, M. Stehlík, and H. Waldl (2009). Filling and d-optimal designs for the correlated generalized exponential models. Technical report, IFAS - JKU University.
  • Stehlík, M. (2007). D-optimal designs and equidistant designs for stationary processes. In J. López-Fidalgo and B. Rodríguez-Díaz, J.M.and Torsney (Eds.), MODA 8 – Advances in Model-Oriented Design and Analysis , pp. 205–212. Heidelberg: Physica-Verlag.
  • Stehlík, M., J. Rodríguez-Díaz, W. Müller, and J. López-Fidalgo (2008). Optimal allocation of bioassays in the case of parametrized covariance functions: an application in lung’s retention of radioactive particles. Test 17, 56–68.
  • Vaghjiani, G. and A. Ravishankara (1991). New measurement of the rate coefficient for the reaction of OH with methane. Nature 350, 406–409.
  • Zagoraiou, M. and A. Baldi-Antognini (2009). Optimal designs for parameter estimation of the Ornstein-Uhlenbeck process. Applied Stochastic Models in Business and Industry 25, 583–600.