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‘Nearly’ universally optimal designs for models with correlated observations

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  • Dette, Holger
  • Pepelyshev, Andrey
  • Zhigljavsky, Anatoly

Abstract

The problem of determining optimal designs for least squares estimation is considered in the common linear regression model with correlated observations. The approach is based on the determination of ‘nearly’ universally optimal designs, even in the case where the universally optimal design does not exist. For this purpose, a new optimality criterion which reflects the distance between a given design and an ideal universally optimal design is introduced. A necessary condition for the optimality of a given design is established. Numerical methods for constructing these designs are proposed and applied for the determination of optimal designs in a number of specific instances. The results indicate that the new ‘nearly’ universally optimal designs have good efficiencies with respect to common optimality criteria.

Suggested Citation

  • Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:1103-1112
    DOI: 10.1016/j.csda.2013.02.002
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    References listed on IDEAS

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    1. Zhigljavsky, Anatoly & Dette, Holger & Pepelyshev, Andrey, 2010. "A New Approach to Optimal Design for Linear Models With Correlated Observations," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1093-1103.
    2. Radoslav Harman & František Štulajter, 2010. "Optimal prediction designs in finite discrete spectrum linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 281-294, September.
    3. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    4. Dette, Holger & Bretz, Frank & Pepelyshev, Andrey & Pinheiro, José, 2008. "Optimal Designs for Dose-Finding Studies," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1225-1237.
    5. Kiselák, Jozef & Stehlík, Milan, 2008. "Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1388-1396, September.
    6. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2008. "Improving updating rules in multiplicative algorithms for computing D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 312-320, December.
    7. 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.
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    1. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2016. "Optimal designs for regression models with autoregressive errors," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 107-115.

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