Optimal martingale estimating equations in a stochastic process

Abstract

We consider the problem of estimating a structural parameter is fully parametric stochastic processes depending on possibly many additional accessory parameters. Within the class of martingale estimating equations, a most precise equation is sought. We define an appropriate measure of precision based on the inequality of Godambe (1960) and following naturally from the work of Godambe (1985). We elucidate some of its properties, provide a statistical justification for its use and show that the partial score maximises this precision for appropriately structured and regular models. © 1987.