Construction Of Complex Structured Uniform Designs

Uniform design is a common design method in experimental design,which considers the experimental points are uniformly distributed within the experimental domain.Moreover,it is a better factorial experimental design for it can carry out multi-factor and high-level factor experiments with less experimental units.This paper proposes the construction of unform designs under the discrete discrepancy.There are two kinds of construction by algorithmic optimization approach and construction via combinatorial configuration.Here,the basic idea is to construct uniform designs using a common combinatorial configuration,namely partitionable t-designs,which require without any computer search.Moreover,certain complex structures are further studied within the propose uniform designs.It shows that there are nested and sliced sub-designs in some uniform designs,and these sub-designs are also uniform designs under discrete discrepancy.Through Lasso variable selection simulation of the constructed uniform design and random design,it can be seen that the Cp-value obtained by uniform design is closer to E_Cpthan that obtained by random design.It is concluded that the uniform design we constructed is better than the traditional random design.The proposed uniform designs may find many applications in statistics including computer experiments,sequential experiments,drug combination studies and cross-validation.