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Optimal designs for regression models with autoregressive errors

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

Abstract

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal variance of the best linear estimator in the continuous time model and to construct efficient estimators and corresponding optimal designs for finite samples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:116:y:2016:i:c:p:107-115
    DOI: 10.1016/j.spl.2016.04.008
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    References listed on IDEAS

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    1. K. S. Chan & H. Tong, 1987. "A Note On Embedding A Discrete Parameter Arma Model In A Continuous Parameter Arma Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(3), pages 277-281, May.
    2. 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.
    3. 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.
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    Citations

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    Cited by:

    1. Andrey Pepelyshev & Anatoly Zhigljavsky & Antanas Žilinskas, 2018. "Performance of global random search algorithms for large dimensions," Journal of Global Optimization, Springer, vol. 71(1), pages 57-71, May.
    2. Dette, Holger & Schorning, Kirsten & Konstantinou, Maria, 2017. "Optimal designs for comparing regression models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 273-286.
    3. Rodríguez-Díaz, Juan M., 2017. "Computation of c-optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 287-296.
    4. Holger Dette & Martin Kroll, 2022. "Asymptotic equivalence for nonparametric regression with dependent errors: Gauss–Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1163-1196, December.

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