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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.