Optimal supersaturated designs

• Autores: Bradley Jones, Dibyen Majumdar
• Localización: Journal of the American Statistical Association, ISSN 0162-1459, Vol. 109, Nº 508, 2014, págs. 1592-1600
• Idioma: inglés
• DOI: 10.1080/01621459.2014.938810
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider screening experiments where an investigator wishes to study many factors using fewer observations. Our focus is on experiments with two-level factors and a main effects model with intercept. Since the number of parameters is larger than the number of observations, traditional methods of inference and design are unavailable. In 1959 , Box suggested the use of supersaturated designs and in 1962 , Booth and Cox introduced measures for efficiency of these designs including E(s2), which is the average of squares of the off-diagonal entries of the information matrix, ignoring the intercept. For a design to be E(s2)-optimal, the main effect of every factor must be orthogonal to the intercept (factors are balanced), and among all designs that satisfy this condition, it should minimize E(s2). This is a natural approach since it identifies the most nearly orthogonal design, and orthogonal designs enjoy many desirable properties including efficient parameter estimation. Factor balance in an E(s2)-optimal design has the consequence that the intercept is the most precisely estimated parameter. We introduce and study UE(s2)-optimality, which is essentially the same as E(s2)-optimality, except that we do not insist on factor balance. We also provide a method of construction. We introduce a second criterion from a traditional design optimality theory viewpoint. We use minimization of bias as our estimation criterion, and minimization of the variance of the minimum bias estimator as the design optimality criterion. Using D-optimality as the specific design optimality criterion, we introduce D-optimal supersaturated designs. We show that D-optimal supersaturated designs can be constructed from D-optimal chemical balance weighing designs obtained by Galil and Kiefer (1980 , 1982 ), Cheng (1980 ) and other authors. It turns out that, except when the number of observations and the number of factors are in a certain range, an UE(s2)-optimal design is also a D-optimal supersaturated design. Moreover, these designs have an interesting connection to Bayes optimal designs. When the prior variance is large enough, a D-optimal supersaturated design is Bayes D-optimal and when the prior variance is small enough, an UE(s2)-optimal design is Bayes D-optimal. While E(s2)-optimal designs yield precise intercept estimates, our study indicates that UE(s2)-optimal designs generally produce more efficient estimates for the main effects of the factors. Based on theoretical properties and the study of examples, we recommend UE(s2)-optimal designs for screening experiments.