Lower bounds of the wrap-around \(L_2\)-discrepancy and relationships between MLHD and uniform design with a large size

DOI10.1016/j.jspi.2007.10.001zbMath1184.62140OpenAlexW1975360587MaRDI QIDQ1031746

Yong-Dao Zhou, Jian-Hui Ning

Publication date: 30 October 2009

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2007.10.001

zbMATH Keywords

simple random samplingwrap-around \(L_{2}\)-discrepancymidpoint Latin hypercube designU-type design

Mathematics Subject Classification ID

Design of statistical experiments (62K99) Sampling theory, sample surveys (62D05) Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items

An efficient local search-based genetic algorithm for constructing optimal Latin hypercube design ⋮ Choice of optimal second stage designs in two-stage experiments ⋮ Constructing optimal router bit life sequential experimental designs: New results with a case study ⋮ Optimal foldover plans of three-level designs with minimum wrap-around \(L_2\)-discrepancy ⋮ Deterministic construction methods for uniform designs ⋮ Constructing uniform designs: A heuristic integer programming method ⋮ Double moving extremes ranked set sampling design ⋮ Some new lower bounds to centered and wrap-round \(L_2\)-discrepancies ⋮ Optimal foldover plans of asymmetric factorials with minimum wrap-around \(L_2\)-discrepancy ⋮ Measures of uniformity in experimental designs: A selective overview ⋮ New foundations for designing U-optimal follow-up experiments with flexible levels ⋮ A new foldover strategy and optimal foldover plans for three-level design ⋮ Sharp lower bounds of various uniformity criteria for constructing uniform designs ⋮ Tripling of fractional factorial designs ⋮ Uniformity criterion for designs with both qualitative and quantitative factors ⋮ New lower bounds of four-level and two-level designs via two transformations ⋮ A new lower bound for wrap-around \(L_2\)-discrepancy on two and three mixed level factorials ⋮ A Lower Bound for the Wrap-around L₂-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lower bounds for wrap-around \(L_2\)-discrepancy and constructions of symmetrical uniform designs
• Controlling Correlations in Latin Hypercube Samples
• A generalized discrepancy and quadrature error bound
• Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points