CONSISTENCY OF PLUG-IN ESTIMATORS OF UPPER CONTOUR AND LEVEL SETS
研究了用有限个矩不等式或等式条件定义的参数集合的估计问题，给出了插件估计量在豪斯多夫度量下一致的条件，并证明了样本GMM目标函数的最小值集合对总体GMM目标函数的最小值集合的一致性。
This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.