Details

Autor(en) / Beteiligte

• Jensen, D.R.
• Ramirez, D.E.

Titel

Enhanced design efficiency through least upper bounds

Ist Teil von

• Journal of statistical computation and simulation, 2016-06, Vol.86 (9), p.1798-1817

Ort / Verlag

Abingdon: Taylor & Francis

Erscheinungsjahr

2016

Quelle

Taylor & Francis Journals Auto-Holdings Collection

Beschreibungen/Notizen

• Lower and upper spectral bounds are known for positive-definite matrices in under Loewner (Uber monotone Matrixfunktionen. Math Z. 1934;38:177-216) ordering. Lower and upper singular bounds for matrices of order in derive under an induced ordering. These orderings are combined here to the following effects. Given two first-order experimental designs in their upper singular bound enhances both and in that its Fisher Information matrix dominates those for both and thus ordering essentials in Gauss-Markov estimation. Moreover, if and are dispersion matrices for linear estimators under and respectively, then is the spectral lower bound for in . In essence this algorithm identifies elements in complementary to those of and combines these into . Case studies illustrate gains to be made thereby in first and second-order designs. Specifically, two examples demonstrate that designs optimal under separate criteria may be combined into a single design dominating both. In addition, selected examples demonstrate that classical second-order designs may be improved inter se.