Exact computation of the asymptotic variance matrix for a tuple of multinomial distributions with dependent parameters

Abstract

In this paper, we consider a statistical model consisting of an s-tuple of multinomial distributions whose parameters are dependent. This model is used in road safety to study the effect of a measure implemented on a set of s sites comprising a total of r accident severity levels and is depending on a parameter vector of 1+sr components under s equality constraints. The computation of the so important asymptotic variance matrix W requires some numerical matrix inversions which become very complicated for large values of s and r. To circumvent this difficulty, we use Schur complement for the exact analytic inversion and we propose a strategy for calculating W. We illustrate the effectiveness of our approach using simulated data.