Estimating functions and approximate conditional likelihood

The approximate conditional likelihood method proposed by Cox & Reid (1987) is applied to the estimation of a scalar parameter Θ, in the presence of nuisance parameters. The estimating function of Θ based on the approximate conditional likelihood is shown to be preferable to that based on the profile likelihood. A sufficient condition for both approaches to be equivalent is given. The role of parameter orthogonality is emphasized. Several examples including bivariate normal means with known coefficient of variation are presented.