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Nonparametric time trends in optimal design of experiments.

By Lieven Tack and Martina Vandebroek

Abstract

When performing an experiment, the observed responses are often influenced by a temporal trend due to aging of material, learning effects, equipment wear-out, warm-up effects, etc. The construction of run orders that are optimally balanced for time trend effects relies on the incorporation of a parametric representation of the time dependence in the response model. The parameters of the time trend are then treated as nuisance parameters. However, the price one has to pay for by purely parametric modeling is the biased results when the time trend is misspecified. This paper presents a design algorithm for the construction of optimal run orders when kernel smoothing is used to model the temporal trend nonparametrically. The benefits of modeling the time trend nonparametrically are outlined. Besides, the influence of the bandwidth and the kernel function on the performance of the optimal run orders is investigated. The presented design algorithm shows to be very useful when it is hard to model the time dependence parametrically or when the functional form of the time trend is unknown. An industrial example illustrates the practical utility of the proposed design algorithm.Optimal; Trends;

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  1. (2001). (Vt , C)-Optimal Run Orders,"
  2. (1985). A Thermodynamical Approach to the Travelling Salesman Problem: An Efficient Simulation Algorithm,"
  3. (1985). Analysis ofField Experiments by Least Squares Smoothing,"
  4. (1990). Applied Nonparametric Regression,
  5. (1984). Boundary Modification for Kernel Regression,"
  6. (1953). Equation of State Calculation by Fast Computing Machines,"
  7. (1996). Experimental Designs Optimally Balanced for Trend,"
  8. (1971). Factorial Designs, the IX'XI Criterion and Some Related Matters,"
  9. (1988). Kernel Smoothing in Partial Linear Models,"
  10. (1985). Kernels for Nonparametric Curve Estimation,"
  11. (1997). Matrix Algebra From A Statistician's Perspective,
  12. (1996). Modern Heuristic Search Methods.
  13. (1969). Nonparametric Estimation of a Multivariate Probability Density,"
  14. (1977). Nonparametric Estimation of a Smooth Regression Function,"
  15. (1951). On the Experimental Attainment of Optimum Conditions,"
  16. (1990). On Weighted Design Optimality Criteria for Polynomial and Smoothing Spline Response Surfaces,"
  17. (1984). Optimal Designs for Nonparametric Regression,"
  18. (1983). Optimization by Simulated Annealing,"
  19. (1989). Sequential Design for Nonparametric Regression,"
  20. (1990). Sequential Design for the Nonparametric Regression of Curves and Surfaces,"
  21. (1979). Smoothing Noisy Data With Spline Functions,"
  22. (1960). Some New Three Level Designs for the Study of Quantitative Variables,"
  23. (1980). Trend-Free Block Designs: Theory,"
  24. (2000). Trend-resistant and Cost-efficient Fixed or Random Block Designs," Under revision.
  25. (2000). Trend-resistant Designs under Budget Constraints,"
  26. (1989). When Optimal Designs for Polynomial Regression are Optimal for Smoothing Spline Models,"

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