The Use of the Tetrachoric Series for Evaluating Multivariate Normal Probabilities.
Abstract
The tetrachoric series is a technique for evaluating multivariate normal probabilities frequently cited in the statistical literature. In this paper we have examined the convergence properties of the tetrachoric series and have established the following. For orthant probabilities, the tetrachoric series converges if abs.val.(rho sub ij) < 1/(k-1), < or = i< j < or = k, where rho sub ij are the correlation coefficients of a k-variate normal distribution. The tetrachoric series for orthant probabilities diverges whenever k is even and rho sub ij > 1/(k-1) or k is odd and rho sub ij > 1/(K-2), 1 < or = i < j < or = k. Other specific results concerning the convergence or divergence of this series are also given. The principal point is that the assertion that the tetrachoric series converges for all k > or = 2 and all rho sub ij such that the correlation matrix is positive definite is false.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1979
- Accession Number
- ADA079721
Entities
People
- Andrew P. Soms
- Bernard Harris
Organizations
- University of Wisconsin–Madison