Removing inessential points in c-and A-optimal design

Luc Pronzato (1, 2) , Guillaume Sagnol (3)

1 Laboratoire I3S - SIS - Signal, Images et Systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
3 Institut für Mathematik [Berlin]

A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal design. Elimination rules for A-optimal design are obtained as a byproduct. When implemented within an optimization algorithm, each inequality gives a screening test that may provide a substantial acceleration by reducing the size of the problem online. Several examples are presented with a multiplicative algorithm to illustrate the effectiveness of the approach.

Mots clés: Inessential Point; Screening Test; Support Point; A-optimal design; c-optimal design

Domaines: Statistiques [math.ST]

Luc Pronzato, Guillaume Sagnol. Removing inessential points in c-and A-optimal design. Journal of Statistical Planning and Inference, 2021, 213, pp.233-252. ⟨10.1016/j.jspi.2020.11.011⟩. ⟨hal-02868664⟩