A study of uniformity pattern for extended designs

ABSTRACT

The objective of this paper is to investigate the issue of projection discrepancy for extended U-type or nearly U-type extended designs along the line of Fang and Qin (2005) based on the centered L₂-discrepancy proposed in Hickernell (1998). Extended designs are obtained through augmenting optimally few runs (or points) to an optimal U-type design. Lower bounds to projection discrepancy with reference to the centered L₂-discrepancy of extended designs have been obtained. Some illustrative examples are also provided.

KEYWORDS:

• Centered L₂-discrepancy
• lower bound
• projection discrepancy
• two-level uniform design

MATHEMATICS SUBJECT CLASSIFICATION:

• 62K15
• 62K10
• 62K99

Acknowledgments

We would like to thank the referees for their helpful and constructive comments and suggestions.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (Nos. 11271147, 11471135, and 11471136).