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Optimal designs for comparing regression models with correlated observations

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  • Dette, Holger
  • Schorning, Kirsten
  • Konstantinou, Maria

Abstract

The problem under investigation is that of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time models as a stochastic integral, a pair of linear unbiased estimators with corresponding optimal designs for finite sample size is constructed. This pair minimises the width of the confidence band for the difference between the estimated curves in a class of linear unbiased estimators approximating the stochastic integrals and is very close to the pair of weighted least squares estimators with corresponding optimal design. Thus results readily available in the literature are extended to the case of correlated observations and an easily implementable solution is provided which is practically non distinguishable from the weighted least squares estimators. The advantages of using the proposed pairs of estimators with corresponding optimal designs for the comparison of regression models are illustrated via several numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:113:y:2017:i:c:p:273-286
    DOI: 10.1016/j.csda.2016.06.017
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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. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    4. 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.
    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.
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    Cited by:

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    2. Chang-Yu Liu & Xin Liu & Rong-Xian Yue, 2024. "Locally optimal designs for comparing curves in generalized linear models," Statistical Papers, Springer, vol. 65(5), pages 3181-3201, July.

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