Estimating Equations in the Presence of a Nuisance Parameter

Abstract

Estimating equations for a real parameter θ which indexes a family of densities p(x, θ) were considered in the note by Godambe (Ann. Math. Statist. 31 (1960) 1208-1211). An optimality property of the equation ∂ log p/∂ θ = 0 among unbiased estimating equations was established. In this paper an analogous result is proved for estimation of a real parameter θ1 in the presence of a nuisance parameter θ2.