Robustness of definitive screening composite designs to missing observations

Abstract

Missing observations are unavoidable in most experimental situation and it is necessary to develop efficient designs that could keep the effect of the missing observations as minimal as possible. In this paper, based on definitive screening composite designs (DSCDs) of Zhou and Xu (Journal of the American Statistical Association 112 (520):1675–83, 2017), definitive screening minimax loss designs denoted by DSCMDs are constructed, which are more robust to one missing design point. These newly constructed designs were compared with some existing composite designs (central composite designs (CCDs), orthogonal array composite designs (OACDs), orthogonal array composite minimax loss designs (OACMs), definitive screening composite designs (DSCDs)) used for estimating the parameters of a second order model, in terms of the D-efficiency and generalized scaled standard deviation. The results showed that the DSCMDs are more robust to missing observation than the existing composite designs considered in this paper when compared in of terms of the D-efficiency and generalized scaled standard deviation.

Keywords:

• Definitive screening composite designs
• central composite designs
• D-efficiency
• generalized scaled standard deviation
• minimax loss criterion