Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities
Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities
复制标题
凸矩不等式定义的模型的渐近有效估计
DOI：
10.3982/ecta10017
复制
发表时间：
2014
期刊：
影响因子：
6.1
通讯作者：
Andrés Santos
中科院分区：
文献类型：
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作者：
Hiroaki Kaido;Andrés Santos
本文研究了部分识别模型的有效估计，这些模型由在感兴趣的参数上是凸的矩不等式定义。在这种情况下，被识别的集合本身是凸的，因此它的支持函数完全表征。在此条件下，尽管支持函数是一个无限维参数，但支持函数允许有√n个一致正则估计。然后推导了其估计的半参数效率界，并证明了任何达到该效率界的正则估计也必须最小化一大类渐近损失函数。此外，我们证明了“插入式”估计器是有效的，并设计了一个一致的自举过程来估计其极限分布。我们研究的设置与Beresteanu和Molinari（2008）以及Bontemps， Magnac和Maurin（2012）研究的不完全线性模型有关，这进一步使我们能够为该问题建立他们提出的估计器的半参数效率。
This paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest. In such a setting, the identified set is itself convex and hence fully characterized by its support function. We provide conditions under which, despite being an infinite dimensional parameter, the support function admits √n‐consistent regular estimators. A semiparametric efficiency bound is then derived for its estimation, and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions. In addition, we show that the “plug‐in” estimator is efficient, and devise a consistent bootstrap procedure for estimating its limiting distribution. The setting we examine is related to an incomplete linear model studied in Beresteanu and Molinari (2008) and Bontemps, Magnac, and Maurin (2012), which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem.
DOI：
10.2139/ssrn.1484713
发表时间：
2009-10
期刊：
Yale: Cowles Foundation Working Papers
影响因子：
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作者：
C. Ai;Xiaohong Chen
通讯作者：
C. Ai;Xiaohong Chen