63
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

A Uniform Bound on a Combinatorial Central Limit Theorem for Randomized Orthogonal Array Sampling Designs

&
Pages 243-255 | Received 18 May 2005, Accepted 02 May 2007, Published online: 10 Mar 2008

REFERENCES

  • Chen , L.H.Y. 1986 . The rate of convergence in a central limit theorem for dependent random variables with arbitrary index set . IMA Preprint Series #243, University of Minnesota .
  • Chen , L.H.Y. , and Shao , Q.M. 2001 . A non-uniform Berry Esseen bound via Stein's method . Probab. Theory Related Fields 20 : 236 – 254 .
  • Davis , P.J. , and Rabinowitz , P. 1984 . Methods of Numerical Integration. , 2nd ed. Academic Press , Orlando , FL .
  • Evans , M. , and Swartz , T. 2000 . Approximating Integrals via Monte–Carlo and Deterministic Methods . Oxford Univ. Press .
  • Neammanee , K. , and Suntornchost , J. 2005. A uniform bound in a combinatorial central limit theorem. Stochastics. Analysis and Applications 23 3:1–20.
  • Loh , W.L. 1996 . A combinatorial central limit theorem for randomized orthogonal array sampling designs . Ann. Statist. 24 : 1209 – 1224 .
  • Hall , M. Jr. 1967 . Combinatorial Theory . Blaisdell publishing company .
  • 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 .
  • Niederreiter , H. 1992 . Random Number Generation and Quasi–Monte Carlo Methods . SIAM , Philadelphia .
  • Owen , A.B. 1992a . Orthogonal array for computer experiments, integration and visualization . Statist. Sinica 2 : 439 – 452 .
  • Owen , A.B. 1992b . A central limit theorem for Latin Hypercube sampling . J.R. Statist. Soc. Ser. B 54 : 541 – 551 .
  • Owen , A.B. 1997a . Monte-Carlo variance of scrambled net quadrature . SIAM J. Numer. Anal. 34 : 1884 – 1910 .
  • Owen , A.B. 1997b . Scrambled net variance for integrals of smooth functions . Ann. Statist. 25 : 1541 – 1562 .
  • Patterson , H.D. 1954 . The errors of lattice sampling . J. Roy. Statist. Soc. Ser. B 16 : 140 – 149 .
  • Raghavarao , D. 1971 . Constructions and Combinatorial Problems in Design of Experiments . John Wiley , New York .
  • Stein , C.M. 1986 . Approximate Computation of Expectations . IMS , Hayward , CA .
  • Stein , M.L. 1987 . Large sample properties of simulations using Latin hypercube sampling . Technometrics 29 : 143 – 151 .
  • Tang , B. 1993 . Orthogonal array-based Latin hypercubes . J. Amer. Statist. Assoc. 88 : 1392 – 1397 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.