Nonparametric Model Calibration Estimation in Survey Sampling
调查抽样中的非参数模型校准估计AI 解读 ↓
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调查抽样中的非参数模型校准估计
- 研究问题
- 当总体所有单位的辅助信息可用时，如何突破线性校准关系，通过非参数预测构建总体参数的调查估计量？
- 方法与思路
- 作者用神经网络和局部多项式估计调查变量与辅助变量的关系，再对总体预测值均值设置权重校准约束。
- 材料陈述的贡献
- 摘要称在适当正则条件下证明设计一致性，推导渐近分布的矩并提出一致方差估计，另开展模拟和溪流生态应用。
- 阅读关注点
- 核对抽样设计、辅助信息可得性、非参数拟合条件，以及预测值校准如何影响设计一致性和方差估计。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；正则条件、模拟数值及方法间比较未提供，不能声称非参数校准普遍更优。
原文摘要
Calibration is commonly used in survey sampling to include auxiliary information at the estimation stage of a population parameter. Calibrating the observation weights on population means (totals) of a set of auxiliary variables implies building weights that when applied to the auxiliaries give exactly their population mean (total). Implicitly, calibration techniques rely on a linear relation between the survey variable and the auxiliary variables. However, when auxiliary information is available for all units in the population, more complex modeling can be handled by means of model calibration; auxiliary variables are used to obtain fitted values of the survey variable for all units in the population, and estimation weights are sought to satisfy calibration constraints on the fitted values population mean, rather than on the auxiliary variables one. In this work we extend model calibration considering more general superpopulation models and use nonparametric methods to obtain the fitted values on which to calibrate. More precisely, we adopt neural network learning and local polynomial smoothing to estimate the functional relationship between the survey variable and the auxiliary variables. Under suitable regularity conditions, the proposed estimators are proven to be design consistent. The moments of the asymptotic distribution are also derived, and a consistent estimator of the variance of each distribution is then proposed. The performance of the proposed estimators for finite-size samples is investigated by means of simulation studies. An application to the assessment of the ecological conditions of streams in the mid-Atlantic highlands in the United States is also carried out.