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Alternative sampling methods for estimating multivariate normal probabilities

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Author Info
Z. Sandor ()
P. Andras (FEW-Econometrie en besliskunde)
Abstract

We study the performance of alternative sampling methods for estimating multivariate normal probabilities through the GHK simulator. The sampling methods are randomized versions of some quasi-Monte Carlo samples (Halton, Niederreiter, Niederreiter-Xing sequences and lattice points) and some samples based on orthogonal arrays (Latin hypercube, orthogonal array and orthogonal array based Latin hypercube samples). In general, these samples turn out to have a better performance than Monte Carlo and antithetic Monte Carlo samples. Improvements over these are large for low-dimensional (4 and 10) cases and still significant for dimensions as large as 50.

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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number 305.

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Date of creation: 2003
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Handle: RePEc:dgr:eureir:2003305

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Related research
Keywords: Simulation Quasi-Monte Carlo (t; m; s)-net Lattice points Multinomial probit;

Find related papers by JEL classification:
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models

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    Other versions:
  2. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October. [Downloadable!] (restricted)
  3. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September. [Downloadable!] (restricted)
    Other versions:
  4. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June. [Downloadable!] (restricted)
  5. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  6. David Revelt & Kenneth Train, 1998. "Mixed Logit With Repeated Choices: Households' Choices Of Appliance Efficiency Level," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 647-657, November. [Downloadable!] (restricted)
  7. Sándor, Zsolt & Train, Kenneth, 2004. "Quasi-random simulation of discrete choice models," Transportation Research Part B: Methodological, Elsevier, vol. 38(4), pages 313-327, May. [Downloadable!] (restricted)
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  8. Stern, Steven, 1992. "A Method for Smoothing Simulated Moments of Discrete Probabilities in Multinomial Probit Models," Econometrica, Econometric Society, vol. 60(4), pages 943-52, July. [Downloadable!] (restricted)
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  12. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134. [Downloadable!] (restricted)
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  13. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August. [Downloadable!]
  14. Kenneth Train, 2003. "Discrete Choice Methods with Simulation," Online economics textbooks, SUNY-Oswego, Department of Economics, number emetr2, March. [Downloadable!]
  15. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-32, November. [Downloadable!] (restricted)
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  16. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  17. Borsch-Supan, Axel & Hajivassiliou, Vassilis A., 1993. "Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models," Journal of Econometrics, Elsevier, vol. 58(3), pages 347-368, August. [Downloadable!] (restricted)
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  18. Geweke, John, 1996. "Monte carlo simulation and numerical integration," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 15, pages 731-800 Elsevier. [Downloadable!] (restricted)
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