Generalized Wald Methods for Testing Nonlinear Implicit and Overidentifying Restrictions
将Wald检验从直接显式参数约束推广到非线性隐式约束，适用于联立方程模型子系统的非线性过度识别结构约束的联合检验，并可通过选择不同矩阵生成一类渐近功效相等的检验。
The W- ld approach to testing direct explicit restrictions on a parameter vector is generalizetd to the case of nonlinear implicit constraints. When applied to subsystems of simultaneous equations models, the generalization enables the symmetric joinit testing of nonlinear overidentufying structural restrictions under very wide cornditions. By varying the choices of certain matrices used to construct the generalized Wald statistic, one produces a whole class of tests which have equal asymptotic power yet whose associated structural coefficient estim,-iators have different asymptotic efficiencies for any given rediuced-form estimator from which they are derived. restrictions on a parameter vector was originally formulated in terms of the unrestricted maximum-likelihood estimator of that vector. Stroud [13] showed clearly how Wald criteria can be defined in terms of consistent asymptotically normal estimators other than maximum likelihood. While this makes the Wald