Orthogonal Array-Based Latin Hypercubes

References

• Bose , R. C. and Bush , K. A. 1952 . “Orthogonal Arrays of Strength Two and Three,” . The Annals of Mathematical Statistics , 23 : 508 – 524 .
   Google Scholar
• Box , G. E. P. and Draper , N. R. 1959 . “A Basis for the Selection of a Response Surface Design,” . Journal of the American Statistical Association , 54 : 622 – 654 .
   Web of Science ®Google Scholar
• Davis , P. J. and Rabinowitz , P. 1984 . Methods of Numerical Integration, , 2nd ed. , Orlando , FL : Academic Press .
   Google Scholar
• Dey , A. 1985 . Orthogonal Fractional Factorial Designs , New York : Halsted .
   Google Scholar
• Hua , L. K. and Wang , Y. 1981 . Applications of Number Theory to Numerical Analysis , Beijing : Springer-Verlag, Science Press .
   Google Scholar
• Iman , R. L. and Conover , W. J. 1982 . “A Distribution-Free Approach to Inducing Rank Correlation Among Input Variables,” . Communications in Statistics, Part B—Simulation and Computation , 11 : 311 – 334 .
   Web of Science ®Google Scholar
• de Launey , W. 1986 . “A Survey of Generalized Hadamard Matrices and Difference Matrices D(k, λ; G) With Large k,” . Utilitas Mathematics , 30 : 5 – 29 .
   Web of Science ®Google Scholar
• McKay , M. D. , Conover , W. J. and Beckman , R. J. 1979 . “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code,” . Technometrics , 21 : 239 – 245 .
   Web of Science ®Google Scholar
• Niederreiter , H. 1978 . “Quasi-Monte Carlo Methods and Pseudo-Random Numbers,” . Bulletin of the American Mathematical Society , 84 : 957 – 1041 .
   Web of Science ®Google Scholar
• Niederreiter , H. 1988 . “Quasi-Monte Carlo Methods for Multidimensional Integration,” . In Numerical Integration III , Edited by: Braß , H. and Hämmerlin , G. 157 – 171 . Basel : Birkhäser Verlag .
   Google Scholar
• Owen , A. 1992 . “Orthogonal Arrays for Computer Experiments, Integration, and Visualization,” . Statistica Sinica , 2 : 439 – 452 .
   Web of Science ®Google Scholar
• Patterson , H. D. 1954 . “The Errors of Lattice Sampling,” . Journal of the Royal Statistical Society , 16 : 140 – 149 . Ser. B
   Google Scholar
• Plackett , R. L. and Burman , J. P. 1946 . “The Designs of Optimum Multifactorial Experiments,” . Biometrika , 33 : 305 – 325 .
   Web of Science ®Google Scholar
• Rao , C. R. 1947 . “Factorial Experiments Derivable from Combinatorial Arrangements of Arrays,” . Journal of the Royal Statistical Society , : 128 – 139 .
   Google Scholar
• Rao , C. R. 1973 . “Some Combinatorial Problems of Arrays and Applications to Design of Experiments,” . In A Survey of Combinatorial Theory , Edited by: Srivastava , J. N. 349 – 359 . Amsterdam : North-Holland .
   Google Scholar
• Stein , M. 1987 . “Large-Sample Properties of Simulations Using Latin Hypercube Sampling,” . Technometrics , 29 : 143 – 151 .
   Web of Science ®Google Scholar
• Sacks , J. and Ylvisaker , D. 1984 . “Some Model Robust Designs in Regression,” . The Annals of Statistics , 12 : 1324 – 1348 .
   Web of Science ®Google Scholar
• Welch , W. J. , Buck , R. J. , Sacks , J. , Wynn , H. P. , Mitchell , T. J. and Morris , M. D. 1992 . “Screening, Predicting, and Computer Experiments,” . Technometrics , 34 : 15 – 25 .
   Web of Science ®Google Scholar
• Welch , W. J. and Sacks , J. 1990 . “A System for Quality Improvement Via Computer Experiments,” , University of Waterloo, Institute for Improvement in Quality and Productivity . Research Report RR-90-09
   Google Scholar
• Wang , J. C. and Wu , C. F. J. 1991 . “An Approach to the Construction of Asymmetrical Orthogonal Arrays,” . Journal of the American Statistical Association , 86 : 450 – 456 .
   Web of Science ®Google Scholar
• Wu , C. F. J. 1989 . “Construction of 2m4n Designs Via a Grouping Scheme,” . The Annals of Statistics , 17 : 1880 – 1885 .
   Web of Science ®Google Scholar
• Wu , C. F. J. , Zhang , R. and Wang , R. 1992 . Construction of Asymmetrical Orthogonal Arrays of the Type OA(sk, sm(s k , s m (s r1 )n1 … (s rt )nt ) . Statistica Sinica , 2 : 203 – 219 .
   Web of Science ®Google Scholar