23
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Control Variates for Monte Carlo Analysis of Nonlinear Statistical Models, I: Overview

&
Pages 1011-1036 | Received 01 Jan 1989, Published online: 27 Jun 2007

Bibliography

  • Adelaar , G. 1986 . “ An empirical investigation of nonlinear least squares with correlated errors ” . Atlanta, Georgia : Georgia Institute of Technology . Unpublished Masters Thesis, School of Industrial and Systems Engineering
  • Anderson , T.W. 1958 . An Introduction to Multivariate Statistical Analysis , New York : John Wiley & Sons .
  • Andrews , D.F. , Bickel , P.J. , Hampel , F.R. , Huber , P.J. , Rogers , W.H. and Tukey , J.W. 1972 . Robust Estimates of Location , Princeton : Princeton University Press .
  • Arnold , H.J. , Bucher , B.D. , Trotter , H.F. and Tukey , J.W. 1956 . “ Monte Carlo techniques in a complex problem about normal samples ” . In Symposium on Monte Carlo Methods , Edited by: Meyer . 80 – 88 . New York : John Wiley & Sons .
  • Bard , Y. 1974 . Nonlinear Parameter Estimation , New York : Academic Press .
  • Bates , D.M. and Watts , D.G. 1980 . Relative curvature measures of nonlinearity . Journal of the Royal Statistical Society , B 42 : 1 – 25 .
  • Beale , E.M.L. 1960 . Confidence regions in non-linear estimation . Journal of the Royal Statistical Society , B 22 : 41 – 88 .
  • Berkson , J. 1950 . Are there two regressions? . Journal of the American Statistical Society , 45 : 164
  • Box , M.J. 1971 . Bias in nonlinear estimation. . Journal of the Royal Statistical Society , B 33 : 171 – 201 .
  • Bratley , P. , Fox , B.L. and Schrage , L.E. 1987 . A Guide to Simulation , New York : Springer-Verlag .
  • Chambers , J.M. 1977 . Computational Methods for Data Analysis , New York : John Wiley & Sons .
  • Cheng , R.C.H. 1978 . Analysis of simulation experiments under normality assumptions . Journal of the Operational Research Society , 29 : 493 – 497 .
  • Clarke , G.P.Y. 1980 . Moments of the least squares estimators in a nonlinear regression model . Journal of the Royal Statistical Society , B 42 : 227 – 237 .
  • Crowder , M.J. 1976 . Maximum likelihood estimation for dependent observations . Journal of the Royal Statistical Society , B 38 : 45 – 53 .
  • Fishman , G.S. 1978 . Principles of Discrete Event Simulation , New York : John Wiley & Sons .
  • Gallant , A.R. 1975 . Nonlinear regression . The American Statistician , 29 : 73 – 81 .
  • Gallant , A.R. 1980 . Explicit estimators of parametric functions in nonlinear regression . Journal of the American Statistical Society , 75 : 182 – 193 .
  • Gallant , A.R . 1987 . Nonlinear Statistical Models , New York : John Wiley & Sons .
  • Gillis , P.R. and Ratkowsky , D.A. 1978 . The behaviour of estimators of the parameters of various yield-density relationships . Biometrics , 34 : 191 – 198 .
  • Grier , D.A. . The Monte Carlo processor: designing and implementing a language for Monte Carlo work . 1985 Proceedings of Computer Science and Statistics: 17th Symposium on the Interface . pp. 217 – 222 . North Holland .
  • Hammersley , J.M. and Handscomb , D.C. 1964 . Monte Carlo Methods , London : Chapman and Hall .
  • Hartley , H.O. 1977 . “ Solution of statistical distribution problems by Monte Cario methods ” . In Statistical Methods for Digital Computers , Edited by: Enslein , Ralston and Wilf . Vol. III , New York : John Wiley & Sons .
  • Johnstone , I.M. and Velleman , P.F. 1985 . Efficient scores, variance decompositions, and Monte Carlo swindles . Journal of the American Statistical Association , 80 : 851 – 862 .
  • Kahn , H. 1956 . “ Use of different Monte Carlo sampling techniques ” . In Symposium on Monte Carlo Methods , Edited by: Meyer . 146 – 190 . New York : John Wiley & Sons .
  • Kleijnen , J.P.C. 1974 . Statistical Techniques in Simulation, Part I , New York : Marcel Dekker .
  • Kleijnen , J.P.C. 1977 . Robustness of a multiple ranking procedure: a Monte Carlo experiment illustrating design and analysis techniques . Communications in Statistics B, Simulation and Computation , 6 : 235 – 262 .
  • Koehler , K.J. 1981 . An improvement of a Monte Carlo technique using asymptotic moments with an application to the likelihood ratio statistic . Communications in Statistics B, Simulation and Computation , 10 : 343 – 357 .
  • Lavenberg , S.S. and Welch , P.D. 1981 . A perspective on the use of control variables to increase the efficiency of Monte Carlo simulations . Management Science , 27 : 322 – 335 .
  • Law , A.M. and Kelton , W.D. 1982 . Simulation Modeling and Analysis , New York : McGraw-Hill .
  • Lewis , P.A.W. , Orav , J.E. and Uribe , L. 1986 . Advanced Simulation and Statistics Package , Monterey, CA : Wadsworth & Brooks/Cole .
  • McGrath, E. and Irving, D. (1973). “Techniques for efficient Monte Carlo simulation, vol. III: variance reduction. ORLC Report SAI-72–509-LJ.
  • Nelson , B.L. 1983 . “ Variance reduction in simulation experiments: a mathematical-statistical framework ” . Purdue University . Unpublished Ph.D. dissertation, School of Industrial Engineering
  • Nelson , B.L. 1987 . A perspective on variance reduction in dynamic simulation experiments . Communications in Statistics B, Simulation and Computation , 16 : 385 – 426 .
  • Nelson , B.L. and Schmeiser , B.W. 1986 . Decomposition of some wellknown variance reduction techniques . Journal of Statistical Computation and Simulation , 23 : 183 – 209 .
  • Porta Nova , A.M. 1985 . “ A generalized approach to variance reduction in discrete-event simulation using control variables ” . Austin, Texas : The University of Texas . Ph.D. Dissertation, Department of Mechanical Engineering 78712
  • Ratkowsky , D.A. 1983 . Nonlinear Regression Modeling , New York : Marcel Dekker .
  • Relles , D.A . 1970 . Variance reduction techniques for Monte Carlo sampling from student distributions . Teehnometries , 12 : 499 – 515 .
  • Rothery , P. 1982 . The use of control variates in Monte Carlo estimation of power . Applied Statistics , 31 : 125 – 129 .
  • Rubinstein , R.Y. and Marcus , R. 1985 . Efficiency of multivariate control variates in Monte Carlo simulation . Operations Research , 33 : 661 – 677 .
  • Schruben , L.W and Margolin , B.H. 1978 . Pseudorandom number assignment in statistically designed simulation and distribution sampling experiments . Journal of the American Statistical Association , 73 : 504 – 520 .
  • Shenton , L.R. and Bowman , K.O. 1977 . Maximum Likelihood Estimation in Small Samples , New York : Macmillan .
  • Swain , J.J. 1982 . “ Monte Carlo estimation of the sampling distribution of nonlinear parameter estimators ” . Purdue University . Unpublished Ph.D. Thesis, School of Industrial Engineering
  • Swain , J.J. 1988a . Control variates for Monte Carlo analysis of nonlinear statistical models IV: nonnormal error distributions . Communications in Statistics B, Simulation and Computation , 17 : 251 – 274 .
  • Swain , J.J. 1988b . “ Higher-order approximators for Monte Carlo studies of nonlinear model parameter estimators ” . Atlanta, Georgia : Georgia Institute of Technology . Technical Report J-88–2, School of Industrial and Systems Engineering
  • Swain , J.J and Schmeiser , B.W. 1987 . Monte Carlo estimation of the sampling distribution of nonlinear model parameter estimators . Ánnals of Operations Research , 8 : 245 – 256 .
  • Swain , J.J and Schmeiser , B.W. 1988 . Control variates for Monte Carlo analysis of nonlinear statistical models, II: raw moments and variances . Journal of Statistical Computation and Simulation , 30 : 39 – 56 .
  • Tocher , K.D. 1963 . The Art of Simulation , Princeton, New Jersey : D Van Nostrand Company .
  • Venkatraman , S. and Wilson , J.R. 1986 . The efficiency of control variates in multiresponse simulation . Operations Research Letters , 5 : 37 – 42 .
  • Wilks , S.S. 1962 . Mathematical Statistics , New York : John Wiley & Sons .
  • Wilson , J.R, . 1984 . Variance reduction techniques for digital simulation . American Journal of Mathematical and Management Sciences , 4 : 277 – 312 .
  • Wu , C.F. 1981 . Asymptotic theory of nonlinear least squares estimation . Annals of Statistics , 9 : 501 – 513 .

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.