Empirical Optimality of Coverage Design Criteria for Space-Filling Designs

Baik, Jung-Min

  • Received : 2012.04.19
  • Accepted : 2012.05.09
  • Published : 2012.06.30


This research is to find a design D that minimizes forecast variance in d dimensions over the candidate space ${\chi}$. We want a robust design since we may not know the specific covariance structure. We seek a design that minimizes a coverage criterion and hope that this design will provide a small forecast variance even if the covariance structure is unobservable. The details of an exchange or swapping algorithm and several properties of the parameters of coverage criterion with the unknown correlation structures are discussed.


Coverage criteria;distance-based designs;forecast variance;swapping algorithm


  1. Atkinson, A. C. and Donev, A. N. (1992). Optimum Experimental Designs, Oxford Science Publications, New York.
  2. Baik, J. (1999). Optimization of Distance-Based Criteria for Space-Filling Designs, Thesis of North Carolina State University, Raleigh.
  3. Currin, C., Mitchell, T., Morris, M. and Ylvisaker, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments, Journal of the American Statistical Association, 86, 953-963.
  4. Doehlert, D. H. (1970). Uniform shell designs, Journal of the Royal Statistical Society, Series C, 19, 231-239.
  5. Johnson, M. E., Moore, L. M. and Ylvisaker, D. (1990). Minimax and maximin distance designs, Journal of Statistical Planning and Inference, 26, 131-148.
  6. Kennard, R. W. and Stone, L. A. (1969). Computer aided design of experiments, Technometrics, 11, 137-148.
  7. Kleijnen, J. P. C. (1987). Statistical Tools for Simulation Practitioners, Dekker, New York.
  8. Marengo, E. and Todeschini, R. (1992). A new algorithm for optimal distance-based experimental design, Chemometrics and Intelligent Laboratory Systems, 16, 37-44.
  9. Mitchell, T. J. (1974). An algorithm for the construction of \D-optimal" experimental designs, Technometrics, 16, 203-210.
  10. Nguyen, N.-K. and Miller, A. J. (1992). A review of some exchange algorithms for constructing discrete D-optimal designs, Computational Statistics & Data Analysis, 14, 489-498.
  11. Nychka, D., Piegorsch, W. and Cox, L. (1998). Case Studies in Environmental Statistics, Lecture Notes in Statistics, 132, Springer Verlag, New York.
  12. Sacks, J., Schiller, S. and Welch, W. (1989). Designs for computer experiments, Technometrics, 31, 41-47.
  13. Tobias, R. (1995). SAS QC Software. Volume 2: Usage and Reference. SAS Institute, Inc., Cary, NC.