Closest Moment Estimationunder General Conditions

This paper considers Closest Moment (CM) estimation with a general distance function, and avoids the assumption of nonsingular quadratic local behavior. The results of Manski [1983], Newey [1988], Pötscher and Prucha [1997], and DE Jong and Han [2002] are obtained as special cases. Consistency and a root-n rate of convergence are obtained under mild conditions on the distance function and on the moment conditions. We derive the limit distribution of CM estimators in a general setting, and show that the limit distribution is not necessarily normal. Asymptotic normality is obtained as a special case when the distance function displays nonsingular quadratic behavior.