New matrix-based methods for the analytic evaluation of the multivariate cumulative normal distribution function

In this paper, the authors develop a new matrix-based implementation of the Mendell and Elston (ME) analytic approximation to evaluate the multivariate normal cumulative distribution (MVNCD) function, using an LDLT decomposition method followed by a rank 1 update of the LDLT factorization. The authors' implementation is easy to code for individuals familiar with matrix-based coding. Further, the authors' new matrix-based implementation for the ME algorithm allows them to efficiently write the analytic matrix-based gradients of the approximated MVNCD function with respect to the abscissae and correlation parameters, an issue that is important in econometric model estimation. In addition, the authors propose four new analytic methods for approximating the MVNCD function. The paper then evaluates the ability of the multiple approximations for individual MVNCD evaluations as well as multinomial probit model estimation. As expected, in the authors' tests for evaluating individual MVNCD functions, the authors found that the traditional GHK approach degrades rapidly as the dimensionality of integration increases. Concomitant with this degradation in accuracy is a rapid increase in computational time. The analytic approximation methods are also much more stable across different numbers of dimensions of integration, and even the simplest of these methods is superior to the GHK-500 beyond seven dimensions of integration. Based on all the evaluation results in this paper, the authors recommend the new Two-Variate Bivariate Screening (TVBS) method proposed in this paper as the evaluation approach for MVNCD function evaluation.

Language

  • English

Media Info

Subject/Index Terms

Filing Info

  • Accession Number: 01662821
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Feb 20 2018 2:35PM