Nonparametric estimating equations based on a penalized information criterion

It has recently been observed that, given the mean-variance relation, one can improve on the accuracy of the quasi-likelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for large samples does the improvement become evident. The author proposes a nonparametric estimating equation that does not depend on the estimation of such moments, but instead on the penalized minimization of asymptotic variance. His method provides a strong improvement over the quasi-likelihood estimator and the adaptive estimators, for a wide range of sample sizes.