调查中的内生后分层：用样本拟合模型进行分类
Endogenous post-stratification in surveys: classifying with a sample-fitted model
摘要：
当分类辅助信息可从调查之外的来源获得时，后分层经常用于提高调查估计量的精度。在自然资源调查中，这类信息往往是从遥感数据中获得的，按类别分类并以像素地图的形式显示。这些地图可以基于拟合到样本数据的分类模型来构建。基于从样本数据中得出的类别对样本数据进行后分层（"内生后分层“）违反了标准的后分层假设，即观察结果被准确地分类到后分层中，并且后分层人口计数是已知的。对于样本拟合的广义线性模型，通过将模型预测的范围划分为预定的区间来构造后层，推导出内生后层估计的性质。在较弱的条件下建立了内生后层估计的设计相合性。在超总体模型下，建立了内生后分层估计的相合性和渐近正态性，证明了它与传统的固定层后分层估计具有相同的渐近方差.模拟实验表明，实际效果的第一次拟合模型的调查数据后分层是小的，即使是相对较小的样本量。
英文摘要：
Post-stratification is frequently used to improve the precision of survey estimators when categorical auxiliary information is available from sources outside the survey. In natural resource surveys, such information is often obtained from remote sensing data, classified into categories and displayed as pixel-based maps. These maps may be constructed based on classification models fitted to the sample data. Post-stratification of the sample data based on categories derived from the sample data (``endogenous post-stratification'') violates the standard post-stratification assumptions that observations are classified without error into post-strata, and post-stratum population counts are known. Properties of the endogenous post-stratification estimator are derived for the case of a sample-fitted generalized linear model, from which the post-strata are constructed by dividing the range of the model predictions into predetermined intervals. Design consistency of the endogenous post-stratification estimator is established under mild conditions. Under a superpopulation model, consistency and asymptotic normality of the endogenous post-stratification estimator are established, showing that it has the same asymptotic variance as the traditional post-stratified estimator with fixed strata. Simulation experiments demonstrate that the practical effect of first fitting a model to the survey data before post-stratifying is small, even for relatively small sample sizes.
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