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Optimal designs subject to cost constraints in simultaneous equations models

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  • Víctor Casero-Alonso
  • Jesús López-Fidalgo

Abstract

A procedure based on a multiplicative algorithm for computing optimal experimental designs subject to cost constraints in simultaneous equations models is presented. A convex criterion function based on a usual criterion function and an appropriate cost function is considered. A specific L-optimal design problem and a numerical example are taken from Conlisk (J Econ 11:63–76, 1979 ) to compare the procedure. The problem would need integer nonlinear programming to obtain exact designs. To avoid this, he solves a continuous nonlinear programming problem and then he rounds off the number of replicates of each experiment. The procedure provided in this paper reduces dramatically the computational efforts in computing optimal approximate designs. It is based on a specific formulation of the asymptotic covariance matrix of the full-information maximum likelihood estimators, which simplifies the calculations. The design obtained for estimating the structural parameters of the numerical example by this procedure is not only easier to compute, but also more efficient than the design provided by Conlisk. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:4:p:701-713
    DOI: 10.1007/s11749-015-0430-x
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    References listed on IDEAS

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    1. Judea Pearl, 2003. "Statistics and causal inference: A review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 281-345, December.
    2. 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.
    3. L. Imhof & J. Lopez‐Fidalgo & W. K. Wong, 2001. "Efficiencies of Rounded Optimal Approximate Designs for Small Samples," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(3), pages 301-318, November.
    4. Conlisk, John, 1979. "Design for simultaneous equations," Journal of Econometrics, Elsevier, vol. 11(1), pages 63-76, September.
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