摘要翻译：
研究了由一般矩约束定义的半参数有效界和参数的有效估计。识别依赖于包含关于缺失变量分布的信息的辅助数据，该信息以在主数据库和辅助数据库中都观察到的代理变量为条件，当这种分布对于两个数据集是公共的时。辅助样本可以独立于主样本，也可以是其子集。对于这两种情况，当给定代理变量的丢失数据概率未知、已知或属于正确指定的参数族时，我们导出了界。我们发现，当两个样本独立时，条件概率不是辅助的。对于所有情况，我们讨论了有效的半参数估计。与基于逆概率加权的估计器相比，基于条件期望投影的估计器需要更温和的正则性条件。
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英文标题：
《Semiparametric efficiency in GMM models with auxiliary data》
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作者：
Xiaohong Chen, Han Hong, Alessandro Tarozzi
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is not ancillary when the two samples are independent. For all cases, we discuss efficient semiparametric estimators. An estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting.
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PDF链接：
https://arxiv.org/pdf/705.0069