Information matrix computation from conditional information via normal approximation

Abstract

This paper provides a method for computing the asymptotic covariance matrix from a likelihood function with known maximum likelihood estimate of the parameters. Philosophically, the basic idea is to assume that the likelihood function should be well approximated by a normal density when asymptotic results about the maximum likelihood estimate are applied for statistical inference. Technically, the method makes use of two facts: the information for a one-dimensional parameter can be well computed when the loglikelihood is approximately quadratic over the range corresponding to a small positive confidence interval; and the covariance matrix of a normal distribution can be obtained from its one-dimensional conditional distributions whose sample spaces span the sample space of the joint distribution. We illustrate the method with its application to a linear mixed-effects model.