Weighted symmetrized centered discrepancy for uniform design

作者：He, Lanlan; Qin, Hong; Ning, Jianhui^*

来源：COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2022, 51(8): 4509-4519.

DOI：10.1080/03610918.2020.1744063

• Cover volume
• Uniform design
• Variable selection
• Weighted symmetrized centered discrepancy

Uniformity and projection uniformity are very important criteria in space-filling design and studied by many authors. In this paper, a new criterion, called weighted symmetrized centered discrepancy (WSCD), is put forwarded for measuring the uniformity of design array. Firstly, a new kernel function is deduced by symmetrizing the reproducing kernel of centered L-2 discrepancy (CD). The new criterion WSCD is generated from the symmetrized the reproducing kernel, which make it avoid the well-known shortcomings of CD. Secondly, the customized weights are set to all the sub-dimensions to conform with the Effect Hierarchy principle. The WSCD has similar computation formula with the popularly used discrepancies, hence all the construction methods for uniform design still work. Thirdly, the weights choice is also discussed, and a practical suggestion is made. A naive empirical comparison is also conducted to show that the new criterion performs better than those existed discrepancies in the variable screening.