ESTIMATION OF REGRESSION-COEFFICIENTS WHEN SOME REGRESSORS ARE NOT ALWAYS OBSERVED
ESTIMATION OF REGRESSION-COEFFICIENTS WHEN SOME REGRESSORS ARE NOT ALWAYS OBSERVED
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DOI：
10.2307/2290910
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发表时间：
1994-09-01
影响因子：
3.7
通讯作者：
ZHAO, LP
中科院分区：
文献类型：
--
作者：
ROBINS, JM;ROTNITZKY, A;ZHAO, LP
在应用问题中，通常为给定一组回归量的响应的条件均值指定一个模型。由于设计或偶然的原因，一些研究对象可能缺少回归量的子集。在本文中，我们提出了一类新的基于逆概率加权估计方程的半参数估计，当数据在Rubin意义下随机缺失且缺失概率已知或可以参数化建模时，它们对条件平均模型的参数向量α(0)是一致的。我们表明,我们班上最优估计量的渐近方差达到半参数方差的模型首先表明我们的估计问题是一个普遍问题的特殊情况任意半参数模型中参数估计的随机数据丢失和观察完整数据的概率有界远离0,然后推导表示有效得分,半参数方差约束,以及在这个更一般的估计问题中任意正则渐近线性估计量的影响函数。由于最优估计量依赖于生成数据的未知概率律，我们提出了局部和全局自适应半参数有效估计量。我们将我们类中的估计量与先前提出的估计量进行比较。我们证明了在我们的类中，每个先前的估计量是渐近等价于一些通常是低效的估计量。这个等价性是一个命题的结果，该命题陈述了α(0)的每一个正则渐近线性估计量与我们类中的某个估计量渐近等价。我们在一个小型模拟研究中比较了各种估计器，并提出了一些实用的建议。
In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose anew class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector alpha(0) of the conditional mean model when the data are missing at random in the sense of Rubin and the missingness probabilities are either known or can be parametrically modeled. We show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0, and then deriving a representation for the efficient score, the semiparametric variance bound, and the influence function of any regular, asymptotically linear estimator in this more general estimation problem. Because the optimal estimator depends on the unknown probability law generating the data, we propose locally and globally adaptive semiparametric efficient estimators. We compare estimators in our class with previously proposed estimators. We show that each previous estimator is asymptotically equivalent to some, usually inefficient, estimator in our class. This equivalence is a consequence of a proposition stating that every regular asymptotic linear estimator of alpha(0) is asymptotically equivalent to some estimator in our class. We compare various estimators in a small simulation study and offer some practical recommendations.