Construction of nearly orthogonal Latin hypercube designs

详细信息    查看全文

• 作者：Ifigenia Efthimiou (1)
  Stelios D. Georgiou (1) (2)
  Min-Qian Liu (3)
  
  1. Department of Mathematics ; University of the Aegean ; Karlovassi ; 83200聽 ; Samos ; Greece
  2. School of Mathematical and Geospatial Sciences ; RMIT University ; Melbourne ; VIC ; 3001 ; Australia
  3. LPMC and Institute of Statistics ; Nankai University ; Tianjin ; 300071 ; China
  
• 关键词：Periodic autocorrelation function ; Circulant matrix ; Computer experiment ; 62K05 ; 62K20
• 刊名：Metrika
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：78
• 期：1
• 页码：45-57
• 全文大小：180 KB
• 参考文献：1. Ai MY, He YZ, Liu SM (2012) Some new classed of orthogonal Latin hypercube designs. J Stat Plan Inference 142:2809鈥?818 CrossRef
  2. Bingham D, Sitter RR, Tang B (2009) Orthogonal and nearly orthogonal designs for computer experiments. Biometrika 96:51鈥?5 CrossRef
  3. Butler NA (2001) Optimal and orthogonal Latin hypercube designs for computer experiments. Biometrika 88:847鈥?57 CrossRef
  4. Cioppa TM, Lucas TW (2007) Efficient nearly orthogonal and spaced-filling Latin hypercubes. Technometrics 49:45鈥?5 CrossRef
  5. Fang KT, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Chapman and Hall/CRC, New York
  6. Georgiou SD (2009) Orthogonal Latin hypercube designs from generalized orthogonal designs. J Stat Plan Inference 139:1530鈥?540 CrossRef
  7. Georgiou SD, Efthimiou I (2014) Some classes of orthogonal Latin hypercube designs. Stat Sin 24:101鈥?20
  8. Georgiou SD, Koukouvinos C, Liu MQ (2014) U-type and column-orthogonal designs for computer experiments. Metrika. doi:10.1007/s00184-014-0486-8
  9. Georgiou SD, Stylianou S (2011) Block-circulant matrices for constructing optimal Latin hypercube designs. J Stat Plan Inference 141:1933鈥?943 CrossRef
  10. Georgiou SD, Stylianou S (2012) Corrigendum to: Block-circulant matrices for constructing optimal Latin hypercube designs. J Stat Plan Inference 142:1623鈥?623 CrossRef
  11. Geramita AV, Seberry J (1979) Orthogonal designs: quadratic forms and Hadamard matrices. Marcel Dekker, New York
  12. Hernandez AS, Lucas TW, Carlyle M (2012) Constructing nearly orthogonal Latin hypercubes for any nonsaturated run-variable combination. ACM Trans Model Comput Simul 22:1鈥?7 CrossRef
  13. Kharaghani H (2000) Arrays for orthogonal designs. J Comb Des 8:166鈥?73 CrossRef
  14. Lin CD, Bingham D, Sitter RR, Tang B (2010) A new and flexible method for constructing designs for computer experiments. Ann Stat 38:1460鈥?477 CrossRef
  15. Lin CD, Mukerjee R, Tang B (2009) Construction of orthogonal and nearly orthogonal Latin hypercubes. Biometrika 96:243鈥?47 CrossRef
  16. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 16:239鈥?45
  17. Owen AB (1994) Controlling correlations in Latin hypercube samples. J Am Stat Assoc 89:1517鈥?522 CrossRef
  18. Pang F, Liu MQ, Lin DKJ (2009) A construction method for orthogonal Latin hypercube designs with prime power levels. Stat Sin 19:1721鈥?728
  19. Steinberg M, Lin DKJ (2006) A construction method for orthogonal Latin hypercube designs. Biometrika 93:279鈥?88 CrossRef
  20. Sun FS, Liu MQ, Lin DKJ (2009) Construction of orthogonal Latin hypercube designs. Biometrika 96:971鈥?74 CrossRef
  21. Sun FS, Liu MQ, Lin DKJ (2010) Construction of orthogonal Latin hypercube designs with flexible run sizes. J Stat Plan Inference 140:3236鈥?242 CrossRef
  22. Sun FS, Pang F, Liu MQ (2011) Construction of column-orthogonal designs for computer experiments. Sci China Math 54:2683鈥?692 CrossRef
  23. Tang B (1998) Selecting Latin hypercubes using correlation criteria. Stat Sin 8:965鈥?77
  24. Viana FAC, Venter G, Balabanov V (2010) An algorithm for fast optimal Latin hypercube design of experiments. Int J Numer Methods Eng 82:135鈥?56
  25. Yang JY, Liu MQ (2012) Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Stat Sin 22:433鈥?42
  26. Yin YH, Liu MQ (2013) Orthogonal Latin hypercube designs for Fourier polynomial models. J Stat Plan Inference 143:307鈥?14 CrossRef
  27. Ye KQ (1998) Orthogonal column Latin hypercubes and their application in computer experiments. J Am Stat Assoc 93:1430鈥?439 CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X

文摘

The Latin hypercube design (LHD) is a popular choice of experimental design when computer simulation is used to study a physical process. In this paper, we propose some methods for constructing nearly orthogonal Latin hypercube designs (NOLHDs) with 2, 4, 8, 12, 16, 20 and 24 factors having flexible run sizes. These designs can be very useful when orthogonal Latin hypercube designs (OLHDs) of the needed sizes do not exist.