Nonparametric model calibration estimation in survey sampling
成果类型：
Article
署名作者：
Montanari, GE; Ranalli, MG
署名单位：
University of Perugia
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214505000000141
发表日期：
2005
页码：
1429-1442
关键词：
neural-networks
regression
variance
DESIGN
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.