Estimation under cross-classified sampling with application to a childhood survey

TL;DR

This paper develops a theoretical framework for estimation under cross-classified sampling, analyzing the efficiency, variance estimation, and practical application in a childhood survey, with comparisons to traditional methods.

Contribution

It introduces a general estimation theory for cross-classified sampling, including variance estimators and practical recommendations for survey analysis.

Findings

Cross-classified sampling often less efficient than two-stage design.

Proposed variance estimators are unbiased and practical.

Application to ELFE survey demonstrates real-world utility.

Abstract

The cross-classified sampling design consists in drawing samples from a two-dimension 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 ELFE survey, 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 super-population model. The proposed estimators are compared for totals and ratios on simulated data. An application on real data from the ELFE survey is also presented, and we make some recommendations. Supplementary materials are available online.