We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, that is, when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of sufficiency and minimality help pin down a desirable one. If estimation of minimal sufficient underlying parameters is inefficient, it introduces noise in the corresponding estimation of weakly regular parameters, whence we can improve the estimators by local asymptotic Rao–Blackwellization. We call an estimator weakly efficient if it does not admit such improvement. New weakly efficient estimators are presented in linear IV and nonlinear regression models. Simulation of a linear IV model demonstrates how 2SLS and optimal IV estimators are improved.

中文翻译：

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半参数模型中的弱辨识理论

我们提供半参数模型中的弱辨识的一般表述和效率概念。当参数为弱规则参数时，即局部为零阶均质时，就会出现弱识别。发生这种情况时，证明不可能进行一致或等方的估计。然后，我们表明存在一个基本的常规参数，该参数可以完全表征弱常规参数。尽管此参数不是唯一的，但是充分性和最小性的概念有助于确定所需的参数。如果最小的足够基本参数的估计效率低下，则会在相应的弱规则参数估计中引入噪声，从而可以通过局部渐近Rao-Blackwellization来改进估计量。如果估算者不接受这种改进，则称其效率较弱。在线性IV和非线性回归模型中提出了新的弱有效估计器。线性IV模型的仿真演示了如何改善2SLS和最佳IV估计量。