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Optimal designs for calibration of orientations |
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| Authors: | Hwashin H. Shin Glen Takahara Duncan J. Murdoch |
| Affiliation: | 1. Air Health Effects Division, Health Canada Ottawa, Ontario, Canada K1A 0K9 &McLaughlin Centre for Population Health Risk Assessment University of Ottawa, Ottawa, Ontario Canada K1N 6N5;2. Department of Mathematics and Statistics Queen's University, Kingston, Ontario Canada K7L 3N6;3. Department of Statistical and Actuarial Science University of Western Ontario, London, Ontario Canada N6A 5B7 |
| Abstract: | This paper concerns designed experiments involving observations of orientations following the models of Prentice (1989) and Rivest &Chang (2006). The authors state minimal conditions on the designs for consistent least squares estimation of the matrix parameters in these models. The conditions are expressed in terms of the axes and rotation angles of the design orientations. The authors show that designs satisfying U1 + … + Un = 0 are optimal in the sense of minimizing the estimation error average angular distance. The authors give constructions of optimal n‐point designs when n ≥ 4 and they compare the performance of several designs through approximations and simulation. |
| Keywords: | Angular distance calibration optimal design orientations |