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Simulation of Multivariate Normal Rectangle Probabilities: Theoretical and Computational Results

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Abstract

An extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral P({bold B};mu,Omega) = integral_{a}^{b} n(v - mu, Omega)dv = E_{V}{bold 1}(V in {bold B}), where V is a m-dimensional normal vector with mean mu, covariance matrix , and density n(v - mu Omega)and 1(V in {bold B}) is an indicator for the event B = {V | a

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File URL: http://cowles.econ.yale.edu/P/cd/d10a/d1021-r.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1021R.

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Length: 43 pages
Date of creation: Oct 1994
Date of revision:
Publication status: Published in Journal of Econometrics (1996), 72: 85-134
Handle: RePEc:cwl:cwldpp:1021r

Note: CFP 924.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

Keywords: Simulation estimation; Monte Carlo integration; discrete choice models; multinomial probit models; importance sampling; acceptance-rejection; Gibbs resampling;

References

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  1. 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.
  2. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1993. "The Method of Simulated Scores for the Estimation of LDV Models," Working Papers _023, Yale University.
  3. McFadden, Daniel L., 1984. "Econometric analysis of qualitative response models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 24, pages 1395-1457 Elsevier.
  4. 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.
  5. Daniel McFadden, 1987. "A Method of Simulated Moments for Estimation of Discrete Response Models Without Numerical Integration," Working papers 464, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. J. E. Dutt, 1976. "Numerical Aspects of Multivariate Normal Probabilities in Econometric Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 547-561 National Bureau of Economic Research, Inc.
  7. Keane, Michael P, 1994. "A Computationally Practical Simulation Estimator for Panel Data," Econometrica, Econometric Society, vol. 62(1), pages 95-116, January.
  8. McFadden, Daniel & Ruud, Paul A, 1994. "Estimation by Simulation," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 591-608, November.
  9. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
  10. Vassilis A. Hajivassiliou, 1991. "Simulation Estimation Methods for Limited Dependent Variable Models," Cowles Foundation Discussion Papers 1007, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. Hajivassiliou, 1993. "A Simulation Estimation Analysis of the External Debt Crises of Developing Countries," Cowles Foundation Discussion Papers 1057, Cowles Foundation for Research in Economics, Yale University.

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