The cross-classified sampling design consists in drawing samples from a twodimension 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 Horvitz-Thompson 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 Horvitz-Thompson estimator, and several unbiased variance estimators. Facing the problem of possibly negative values, we propose simplified non-negative variance estimators and study their bias under a superpopulation 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 are available online.
analysis of variance; Horvitz-Thompson estimator; independence; invariance; Sen-Yates-Grundy estimator; two-stage sampling;
Hélène Juillard, Guillaume Chauvet, and Anne Ruiz-Gazen, “Estimation under cross-classified sampling with application to a childhood survey”, TSE Working Paper, n. 16-659, April 2016.
Hélène Juillard, Guillaume Chauvet, and Anne Ruiz-Gazen, “Estimation under cross-classified sampling with application to a childhood survey”, Journal of the American Statistical Association, vol. 112, n. 518, 2017, pp. 850–858.