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Related Experiment Video

Updated: Mar 19, 2026

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
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Optimal designs in regression with correlated errors.

Holger Dette1, Andrey Pepelyshev2, Anatoly Zhigljavsky2

  • 1Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum, Germany.

Annals of Statistics
|June 25, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces optimal experimental designs for dependent regression models. New estimators achieve high precision, closely matching the best achievable results for interval-dependent data.

Keywords:
BLUEDoob representationGaussian processescorrelated observationslinear regressionoptimal designsigned measures

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Area of Science:

  • Statistics
  • Experimental Design
  • Regression Analysis

Background:

  • Optimal design is crucial for efficient regression modeling, especially with dependent observations.
  • Existing methods may not fully address interval-dependent data challenges.

Purpose of the Study:

  • To provide a comprehensive solution for optimal design in regression models with interval-dependent observations.
  • To develop efficient estimators and experimental designs for such models.

Main Methods:

  • Proposed a class of estimators related to ordinary least-squares.
  • Derived explicit expressions for Best Linear Unbiased Estimators (BLUE) in continuous time models.
  • Developed analytic expressions for optimal designs across various regression models.

Main Results:

  • Asymptotic precision of new estimators matches the BLUE for the entire process trajectory.
  • Finite observation precision is very close to the best achievable.
  • Numerical examples illustrate the effectiveness of the proposed procedure.

Conclusions:

  • The proposed method offers a practical and highly precise approach to optimal design for dependent regression models.
  • This work advances the theory and application of optimal experimental design in statistical modeling.