In this paper, we discuss an optimal sufficient dimension reduction through minimizing a quadratic objective function proposed by Cook and Ni (2005) with singular inner-product matrix. Within a less restrictive class of inner-product matrices, a generalized inverse of the consistent estimator of...

This article reviews a number of recent contributions to estimation and inference for models defined by moment condition restrictions. The particular emphasis is on the generalized empirical likelihood class of estimators as an alternative to the generalized method of moments. Estimation methods...

The generalized method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first order equivalent semi-parametric efficient estimators and tests for conditional moment...