Abstract
If the sample sizen is large enough, then the exact polynomial regression designs obtained by rounding the weights of the approximate D-optimal design to integral multiples of 1/n are D-optimal. This was shown by Šalaevskiî (1966) and Gaffke (1987). In this note, an efficient algorithm to determine the minimum sample sizen d for a polynomial model of degreed is derived from a condition given by Huang (1987). Under an additional assumption we show that the conditions of Gaffke and Huang are equivalent; we verify the additional assumption for polynomial degreed≤40.
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Happacher, M. Exact and approximate D-optimal designs in polynomial regression. Metrika 42, 19–27 (1995). https://doi.org/10.1007/BF01894286
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DOI: https://doi.org/10.1007/BF01894286