M-Estimators Based on Inverse Probability Weighted Estimating Equations with Response Missing at Random
M-Estimators Based on Inverse Probability Weighted Estimating Equations with Response Missing at Random
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DOI：
10.1080/03610920601076917
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
Qihua Wang
中科院分区：
文献类型：
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作者：
Qihua Wang
具有完整数据的 M 估计量的渐近性质被广泛研究。然而，在存在缺失数据的情况下，不能直接应用完整数据的标准推理程序。在本文中，将逆概率加权方法应用于缺失响应问题来定义 M 估计量。 M 估计量的存在是在非常一般的规律性条件下成立的。分别证明了M估计量的一致性和渐近正态性。应用迭代算法来计算 M 估计量。结果表明，一步迭代就足够了，并且所得的一步 M 估计具有与完全迭代的 M 估计器相同的极限分布。
Asymptotic properties of M-estimators with complete data are investigated extensively. In the presence of missing data, however, the standard inference procedures for complete data cannot be applied directly. In this article, the inverse probability weighted method is applied to missing response problem to define M-estimators. The existence of M-estimators is established under very general regularity conditions. Consistency and asymptotic normality of the M-estimators are proved, respectively. An iterative algorithm is applied to calculating the M-estimators. It is shown that one step iteration suffices and the resulting one-step M-estimate has the same limit distribution as in the fully iterated M-estimators.