Decomposition of some weil-known variance reduction techniques Footnote^†

^†Research partially supported by Office of Naval Research contract N00014-79-C-0832.

References

• Bratley , P. , Fox , B.L. and Schrage , L.E. 1983 . A Guide to Simulation , New York : Springer- Verlag .
   Google Scholar
• Cochran , W.G. 1977 . Sampling Techniques , New York : Wiley .
   Google Scholar
• Dubi , A. and Horowitz , Y.S. 1979 . The interpretation of conditional Monte Carlo as a form of importance sampling . SIAM J. Appl. Math , 36 ( 1 ) : 115 – 122 .
   Web of Science ®Google Scholar
• Fishman , G.S. and Huang , B. 1983 . Antithetic variates revisited . Commun. ACM , 26 ( 11 ) : 964 – 971 .
   Web of Science ®Google Scholar
• Granovsky , B.L. 1981 . Optimal formulae of the conditional Monte Carlo . SIAM J. Alg. Discrete Meth , 2 ( 3 ) : 289 – 294 .
   Web of Science ®Google Scholar
• Halton , J.H. and Handscomb , D.C. 1957 . A method for increasing the efficiency of Monte Carlo integration . J. ACM , 4 ( 3 ) : 329 – 340 .
   Web of Science ®Google Scholar
• Hammersley , J.M. and Handscomb , D.C. 1964 . Monte Carlo Methods , London : Chapman and Hall .
   Google Scholar
• Hammersley , J.M. and Mauldon , J. 1956 . General principles of antithetic variates . Proc. Camb. Phil Soc , 52 : 476 – 481 .
   Google Scholar
• Hammersley , J.M. and Morton , K.W. 1956 . A new Monte Carlo technique: Antithetic variates . Proc. Camb. Phil. Soc , 52 : 449 – 475 .
   Google Scholar
• Handscomb , D.C. 1958 . Proof of the antithetic-variates theorem for n>2 . Proc.Camb. Phil Soc , 54 ( 2 ) : 300 – 301 .
   Google Scholar
• Isaki , C.T. 1983 . Variance estimation using auxiliary information . J. Am. Statist. Assoc , 78 ( 381 ) : 117 – 123 .
   Web of Science ®Google Scholar
• Jeruchim , M.C. 1984 . On the application of importance sampling to the simulation of digital satellite and multihop links . IEEE Trans. Communications , 32 ( 10 ) : 1082 – 1088 .
   Web of Science ®Google Scholar
• Kahn , H. 1956 . “ Use of different Monte Carlo sampling techniques ” . In Symposium on Monte Carlo Methods , Edited by: Meyer , M. 146 – 190 . New York : Wiley .
   Google Scholar
• Kleijnen , J. 1974 . Statistical Techniques in Simulation, Part I , New York : Marcel Dekker .
   Google Scholar
• Law , A.M. and Kelton , W.D. 1982 . Simulation Modeling and Analysis , New York : McGraw-Hill Book .
   Google Scholar
• McGrath E. J. Irving D. C. Techniques for efficient Monte Carlo simulation 1973 III Variance Reduction. ORNL Report, SAI-72-509-LJ
   Google Scholar
• Morton , K.W. 1957 . A generalization of the antithetic variate technique for evaluating integrals . J. Math. Physics , 36 ( 3 ) : 289 – 293 .
   Google Scholar
• Nelson , B.L. 1983 . Variance reduction in simulation experiments: A mathematical-statistical framework , Purdue University . Unpublished Ph.D. dissertation, School of Industrial Engineering
   Google Scholar
• Nelson , B.L. and Schmeiser , B.W. 1984a . A mathematical-statistical framework for variance reduction, Part I: Simulation experiments , Purdue University . Research Memorandum 84-4, School of Industrial Engineering
   Google Scholar
• Nelson , B.L. and Schmeiser , B.W. 1984b . A mathematical-statistical framework for variance reduction, Part II: Classes of transformations , Purdue University . Research Memorandum 84-5, School of Industrial Engineering
   Google Scholar
• Rubinstein , R.Y. 1981 . Simulation and the Monte Carlo Method , New York : Wiley .
   Google Scholar
• Trotter , H.F. and Tukey , J.W. . Conditional Monte Carlo for normal samples . Symposium on Monte Carlo Methods . Edited by: Meyer , H. pp. 64 – 79 . New York : Wiley .
   Google Scholar
• Whitt , W. 1976 . Bivariate distributions with given marginals . Ann Statist , 4 : 1280 – 1289 .
   Web of Science ®Google Scholar
• Wilson , J.R. 1979 . Proof of the antithetic variate theorem for unbounded functions . Proc. Camb. Phil. Soc , 86 : 477 – 479 .
   Web of Science ®Google Scholar
• Wilson , J.R. 1983a . Variance reduction: The current state . Math. Comput. Simul , XXV : 55 – 59 .
   Web of Science ®Google Scholar
• Wilson , J.R. 1983b . Antithetic sampling with multivariate inputs . American J. Math.and Mgt. Sci , 3 ( 2 ) : 121 – 144 .
   Google Scholar
• Wilson , J.R. 1984 . Variance reduction techniques for digital simulation . American J. Math. and Mgt. Sci , 4 ( 3/4 ) : 277 – 312 .
   Google Scholar
• Wilson , J.R. and Pritsker , A.A.B. 1984a . Variance reduction in queueing simulation using generalized concomitant variables . J. Statist. Cornput. Simul , 19 ( 3/4 ) : 129 – 153 .
   Google Scholar
• Wilson , J.R. and Pritsker , A.A.B. 1984b . Experimental evaluation of variance reduction techniques for queueing simulation using generalized concomitant variables . Mgt. Sci , 30 ( 12 ) : 1459 – 1472 .
   Web of Science ®Google Scholar