抽样调查中关于模型推断的思考

Idea on Model Inference in Sampling Survey

抽样调查中利用辅助信息建立超总体模型能够有效提高推断总体参数的效率.模型辅助方法的思想是基于抽样设计借助于超总体模型获得对总体参数的有效推断.基于模型推断方法完全是基于超总体模型推断总体参数.平衡样本是指辅助变量的汉森赫维茨估计等于总体总量的真值.对于平衡样本,如果模型的异方差性可以通过辅助变量解释,模型辅助获得的广义回归估计与基于模型的最优无偏估计是一致的,搭建了基于设计推断与基于模型推断的桥梁.由此得出最优抽样策略:平衡抽样设计与HT估计结合是最优策略,包含概率正比于模型残差的标准差.

The use of auxiliary information in the sample survey to establish a super-master model can effectively improve the efficiency of the overall parameter inference. An idea of model-assisted approach is to obtain inference of population parameters based on design by superpopulation. Model based inference meth- od infering population parameters is entirely based on the superpopulation model. Samples such as the Hor- vitz-Thompson estimators for auxiliary variables exactly matching the known population totals are called balanced samples. If the heteroscedasticity of the model is ＂fully explainable＂ by the auxiliary variables,a gen- eralized regression estimator is the same as a best linear unbiased estimator for balanced samples. It is pro- posed that optimal strategies consist of HT estimator and balance sampling with inclusion probabilities which are proportional to the standard deviations of the errors of the model.