A New Characterization of Elfving's Method for High Dimensional Computation
Abstract
We give a new characterization of Elfving's (1952) method for computing c-optimal designs in k dimensions which gives explicit formulae for the k unknown optimal weights and k unknown signs in Elfving's characterization. This eliminates the need to search over these parameters to compute c-optimal designs, and thus reduces the computational burden from solving a family of optimization problems to solving a single optimization problem for the optimal finite support set. We give two illustrative examples: a high dimensional polynomial regression model and a logistic regression model, the latter showing that the method can be used for locally optimal designs in nonlinear models as well.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2011
- DOI:
- 10.48550/arXiv.1110.6623
- arXiv:
- arXiv:1110.6623
- Bibcode:
- 2011arXiv1110.6623B
- Keywords:
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- Mathematics - Statistics Theory;
- Statistics - Methodology;
- 62K05 (Primary) 62J05 (Secondary)
- E-Print:
- 2 figures