Estimating Equations in the Presence of a Nuisance Parameter

Estimating equations for a real parameter $\theta$ which indexes a family of densities $p(x, \theta)$ were considered in the note by Godambe (Ann. Math. Statist. 31 (1960) 1208-1211). An optimality property of the equation $\partial \log p/\partial \theta = 0$ among unbiased estimating equations was established. In this paper an analogous result is proved for estimation of a real parameter $\theta_1$ in the presence of a nuisance parameter $\theta_2$ .Estimating equations for a real parameter $\theta$ which indexes a family of densities $p(x, \theta)$ were considered in the note by Godambe (Ann. Math. Statist. 31 (1960) 1208-1211). An optimality property of the equation $\partial \log p/\partial \theta = 0$ among unbiased estimating equations was established. In this paper an analogous result is proved for estimation of a real parameter $\theta_1$ in the presence of a nuisance parameter $\theta_2$.

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