QUASI PROFILE AND DIRECTED LIKELIHOODS FROM ESTIMATING FUNCTIONS

O. E. BARNDORFF-NIELSEN

Department of Theoretical Statistics, Institute of Mathematics, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark

(Received May 16, 1994; revised January 6, 1995)

Abstract. Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour.

Key words and phrases: Directed likelihood, estimating equations, profile likelihood.