CALIBRATION ESTIMATORS IN SURVEY SAMPLING
CALIBRATION ESTIMATORS IN SURVEY SAMPLING
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DOI：
10.2307/2290268
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发表时间：
1992-06-01
影响因子：
3.7
通讯作者：
SARNDAL, CE
中科院分区：
文献类型：
--
作者：
DEVILLE, JC;SARNDAL, CE
本文研究了在单变量或多变量辅助信息存在下有限总体总量的估计问题。估计相当于给调查数据加上权重。我们专注于几个加权系统，可以与一个给定的辅助信息量，并导出一个加权系统的帮助下的距离测量和一组校准方程。我们简要地提到一个应用程序的情况下，其中的信息包括已知的边际计数在一个双向或多向表，被称为广义耙。广义回归估计量（GREG）是考虑到多变量辅助信息而设计的。通常，该估计量由研究变量y和辅助向量x之间的回归关系证明。但我们注意到，GREG可以通过不同的路线来推导，而不是专注于权重。第k个观测值的普通抽样权为1/pi（k），其中pi（k）是k的包含概率。我们表明，GREG所隐含的权重是尽可能接近，根据给定的距离测量，1/pi（k），同时尊重边条件称为校准方程。这些规定表明，加权辅助变量值的样本总和必须等于该辅助变量的已知总体总和。也就是说，当应用于每个辅助变量时，校准的权重必须给出完美的估计。这是一个吸引许多从业者的一致性检查，因为辅助变量和研究变量之间的强相关性意味着对辅助变量表现良好的权重也应该对研究变量表现良好。GREG有效地使用了辅助信息，因此估计是精确的;然而，各个权重并不总是没有问题。例如，可能出现负权重，在某些应用中，这是没有意义的。在潜在的距离度量中寻找不满的根源是很自然的。因此，我们允许仅满足一组最小要求的替代距离度量。每个距离测量通过校准方程通向特定的加权系统，从而通向新的估计器。这些估计量形成一个家庭的校准估计。我们表明，GREG是一个第一近似的家庭的所有其他成员，都是渐近等价的GREG，和方差估计已经知道的GREG建议用于家庭的任何其他成员。权重的数值特征和计算的简便性成为在估计量之间进行选择的基础。该推理应用于双向频率表已知边缘的校准。在这种情况下，我们的距离测度族导致了一个广义的耙过程族，其中经典的耙比是其中之一。
This article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information. Estimation is equivalent to attaching weights to the survey data. We focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations. We briefly mention an application to the case in which the information consists of known marginal counts in a two- or multi-way table, known as generalized raking. The general regression estimator (GREG) was conceived with multivariate auxiliary information in mind. Ordinarily, this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x. But we note that the GREG can be derived by a different route by focusing instead on the weights. The ordinary sampling weights of the kth observation is 1/pi(k), where pi(k), is the inclusion probability of k. We show that the weights implied by the GREG are as close as possible, according to a given distance measure, to the 1/pi(k) while respecting side conditions called calibration equations. These state that the sample sum of the weighted auxiliary variable values must equal the known population total for that auxiliary variable. That is, the calibrated weights must give perfect estimates when applied to each auxiliary variable. That is a consistency check that appeals to many practitioners, because a strong correlation between the auxiliary variables and the study variable means that the weights that perform well for the auxiliary variable also should perform well for the study variable. The GREG uses the auxiliary information efficiently, so the estimates are precise; however, the individual weights are not always without reproach. For example, negative weights can occur, and in some applications this does not make sense. It is natural to seek the root of the dissatisfaction in the underlying distance measure. Consequently, we allow alternative distance measures that satisfy only a set of minimal requirements. Each distance measure leads, via the calibration equations, to a specific weighting system and thereby to a new estimator. These estimators form a family of calibration estimators. We show that the GREG is a first approximation to all other members of the family; all are asymptotically equivalent to the GREG, and the variance estimator already known for the GREG is recommended for use in any other member of the family. Numerical features of the weights and ease of computation become more than anything else the bases for choosing between the estimators. The reasoning is applied to calibration on known marginals of a two-way frequency table. Our family of distance measures leads in this case to a family of generalized raking procedures, of which classical raking ratio is one.