QUASI-PROFILE LOGLIKELIHOODS FOR UNBIASED ESTIMATING FUNCTIONS

G. ADIMARI AND L. VENTURA

Dipartimento di Scienze Statistiche, Università di Padova, via C. Battisti 241, 35121 Padova, Italy

(Received April 3, 2000; revised October 20, 2000)

Abstract. This paper presents a new quasi-profile loglikelihood with the standard kind of distributional limit behaviour, for inference about an arbitrary onedimensional parameter of interest, based on unbiased estimating functions. The new function is obtained by requiring the corresponding quasi-profile score function to have bias and information bias of order O(1). We illustrate the use of the proposed pseudo-likelihood with an application to robust inference in linear models.

Key words and phrases: Estimating equation, M-estimator, profile likelihood, quasilikelihood, second Bartlett identity.