References
- McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 1979;21:239–245.
- Stein M. Large-sample properties of simulations using Latin hypercube sampling. Technometrics. 1987;29:145–151. doi: 10.1080/00401706.1987.10488205
- Owen AB. A central limit theorem for Latin hypercube sampling. Ann Statist. 1992;22:930–945. doi: 10.1214/aos/1176325504
- Tang B. Orthogonal array-based Latin hypercubes. J Amer Statist Assoc. 1993;88:1392–1397. doi: 10.1080/01621459.1993.10476423
- Loh WL. A combinatorial central limit theorem for randomized orthogonal array sampling designs. Ann Statist. 1996;24:1209–1224. doi: 10.1214/aos/1069362310
- Loh WL. A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments. Ann Statist. 2008;36:1983–2023. doi: 10.1214/07-AOS530
- He X, Qian PZG. A central limit theorem for general orthogonal array based space-filling designs. Ann Statist. 2014;42:1725–1750. doi: 10.1214/14-AOS1231
- Mukerjee R, Wu CFJ. A modern theory of factorial design. Series in statistics. New York: Springer; 2006.
- He X, Qian PZG. Nested orthogonal array-based Latin hypercube designs. Biometrika. 2011;98:721–731. doi: 10.1093/biomet/asr028
- Hwang YD, He X, Qian PZG. Sliced orthogonal array based Latin hypercube designs. Technometrics. 2016;58:50–61. doi: 10.1080/00401706.2014.993092
- He Y, Tang B. Strong orthogonal arrays and associated Latin hypercubes for computer experiments. Biometrika. 2013;100:254–260. doi: 10.1093/biomet/ass065
- He Y, Tang B. A characterization of strong orthogonal arrays of strength three. Ann Statist. 2014;42:115–128. doi: 10.1214/13-AOS1167
- Chen J, Qian PZG. Latin hypercube designs with controlled correlations and multi-dimensional stratification. Biometrika. 2014;101:319–332. doi: 10.1093/biomet/ast062
- Ai M, Kong X, Li K. A general theory for orthogonal array based Latin hypercube sampling. Statist Sin. 2016;26:761–777.
- He X, Qian PZG. A central limit theorem for nested or sliced Latin hypercube designs. Statist Sin. Preprint; 2016. doi: 10.5705/ss.202015.0240.
- Owen AB. Lattice sampling revisited: Monte Carlo variance of means over randomized orthogonal arrays. Ann Statist. 1994;22:930–945. doi: 10.1214/aos/1176325504
- Durret R. Probability: theory and examples. Cambridge: Cambridge University Press; 2010.
- Morris MD, Mitchell TJ. Exploratory designs for computer experiments. J Statist Plan Inference. 1995;43:381–402. doi: 10.1016/0378-3758(94)00035-T
- Qian PZG, Ai M, Wu CFJ. Construction of nested space-filling designs. Ann Statist. 2009;37:3616–3643. doi: 10.1214/09-AOS690
- Qian PZG, Wu CFJ. Sliced space-filling designs. Biometrika. 2009;96:945–956. doi: 10.1093/biomet/asp044
- Ai M, Jiang B, Li K. Construction of sliced space-filling designs based on balanced sliced orthogonal arrays. Statist Sin. 2014;24:1685–1702.
- Owen AB. Controlling correlations in Latin hypercube samples. J R Stat Soc Ser B. 1994;89:1517–1522.