Estimation Under Cross-Classified Sampling With Application to a Childhood Survey

• 成果类型: Article
• 署名作者: Juillard, Helene; Chauvet, Guillaume; Ruiz-Gazen, Anne
• 署名单位: Ecole Nationale de la Statistique et de l'Analyse de l'Information (ENSAI); Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1186028
• 发表日期: 2017
• 页码: 850-858

摘要

The cross-classified sampling design consists in drawing samples from a two-dimensional population, independently in each dimension. Such design is commonly used in consumer price index surveys and has been recently applied to draw a sample of babies in the French Longitudinal Survey on Childhood, by crossing a sample of maternity units and a sample of days. We propose to derive a general theory of estimation for this sampling design. We consider the HorvitzThompson estimator for a total, and show that the cross-classified design will usually result in a loss of efficiency as compared to the widespread two-stage design. We obtain the asymptotic distribution of the HorvitzThompson estimator and several unbiased variance estimators. Facing the problem of possibly negative values, we propose simplified nonnegative variance estimators and study their bias under a super-population model. The proposed estimators are compared for totals and ratios on simulated data. An application on real data from the French Longitudinal Survey on Childhood is also presented, and we make some recommendations. Supplementary materials for this article are available online.