Sliced Space‐Filling Design With Mixtures

In this paper, we introduce a novel framework that uses sliced representative points of distribution functions to construct sliced space‐filling designs for mixture components. Using energy distance decomposition, we first establish a relationship between the representativeness of the full point set and its sliced subsets. Based on this, we propose two contrasting construction methods that prioritize representativeness at either the full set or the subset level. To balance both levels, we further develop a hybrid energy distance criterion and corresponding one‐shot and sequential construction algorithms. An accompanying R package is provided for practical use. We also establish the distributional convergence of the point sets and subsets generated by all three methods. Numerical results show that designs based on sliced representative points achieve significant improvements in both space‐filling performance and predictive accuracy.