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Evaluation of Multivariate Normal Probability Integrals Using a Low Variance Simulator

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  • Breslaw, Jon A

Abstract

This paper describes a low variance simulator of the normal distribution function. The probability integral is evaluated exactly at an initial point specified with a factor analytic covariance structure, so that the integral can be derived using dimension reduction techniques. The line integral between the initial point and the desired point is evaluated using Plackett's identity. A Monte Carlo simulation of this line integral simulator (LIS) with the Geweke-Hajivassiliou-Keane (GHK) simulator demonstrates that for dimensions of ten or less, the LIS outperformed the GHK simulator, typically by an order of magnitude and in some cases by two orders of magnitude. Copyright 1994 by MIT Press.

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  • Breslaw, Jon A, 1994. "Evaluation of Multivariate Normal Probability Integrals Using a Low Variance Simulator," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 673-682, November.
    • Handle: RePEc:tpr:restat:v:76:y:1994:i:4:p:673-82
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    Cited by:

    1. István Deák, 2011. "Efficiency of Monte Carlo computations in very high dimensional spaces," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 177-189, June.
    2. Todd M. Schmit & Brian W. Gould & Diansheng Dong & Harry M. Kaiser & Chanjin Chung, 2003. "The Impact of Generic Advertising on U.S. Household Cheese Purchases: A Censored Autocorrelated Regression Approach," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 51(1), pages 15-37, March.
    3. Deak, Istvan, 1998. "Linear regression estimators for multinormal distributions in optimization of stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 111(3), pages 555-568, December.
    4. Dong, Diansheng & Chung, Chanjin & Kaiser, Harry M., 2001. "Panel Data Double-Hurdle Model: An Application To Dairy Advertising," 2001 Annual meeting, August 5-8, Chicago, IL 20502, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Jacques Huguenin & Florian Pelgrin & Alberto Holly, 2009. "Estimation of multivariate probit models by exact maximum likelihood," Working Papers 0902, University of Lausanne, Institute of Health Economics and Management (IEMS).

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