North-Holland Optimal designs for robust estimation in conditionally contaminated linear models

125 A generalization of the classical A-optimality criterion for designs is derived by defining optimal designs for those asymptotically linear (AL-) estimators which are optimally robust in the sense of minimizing the trace of the covariance matrix under bounded bias in an infinitesimal conditionally contaminated normal linear model. It is proved that the A-optimal designs are also optimal in the generalized, robust sense. For the proof special characterizations of the influence functions of the optimal robust AL-estimators for A-optimal designs and designs with finite support based on characterizations in Hampel (Proe. ASA Stat. Comp. Section, 1978), Krasker (Econometrica 48, 1980) and Kurotschka and Müller (Ann. Statist. 20, 1992) are investigated. In particular a very simple form of optimal influence functions at A-optimal designs is derived. This provides the side reseult that for estimating the whole parameter vector at A-optimal designs the Huber and the Hampel-Krasker estimator coincide. AMS Subject Classification: Primary 62F35, 62K05; secondary 62J05. Key words and phrases: Linear model; infinitesimal contamination neighbourhood; robust estimation