GEOMETRICAL EXPANSIONS FOR THE DISTRIBUTIONS OF THE SCORE VECTOR AND THE MAXIMUM LIKELIHOOD ESTIMATOR

MARIANNE MORA

U.F.R. Sciences Economiques, Université de Paris X Nanterre, 200 Avenue de la République, 92001 Nanterre Cedex, France

(Received April 13, 1989; revised June 2, 1990)

Abstract. In the present note, asymptotic expansions for conditional and unconditional distributions of the score vector are derived. Our aim is to consider these expansions in the light of differential geometry, particularly the theory of derivative strings. Expansions for the distributions of the maximum likelihood estimator are obtained from those for the score vector via transformation, with a view to interpreting from the standpoint of differential geometry the various terms entering the expansions.

Key words and phrases: Geometrical expansions, score vector, maximum likelihood estimator, observed and expected geometries.