Maximum likelihood estimator and singularity of the information matrix
Marco Barnabani · Florence Research (University of Florence) · 2006
When the information matrix is singular the classic asymptotic properties of the maximum likelihood estimator are not clear and an inferential procedure based on it is not viable.In the paper a solution of a loglikelihood equation appropriately penalized is shown to be consistent and asymptotically normal distributed with variancecovariance matrix approximated by the Moore-Penrose pseudoinverse of the information matrix.These properties allow one to get a quadratic function based on a standard Chisquare distribution for hypothesis testing.A simulation applied to a simplified Engle's model is presented to support the theoretical results.