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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.
Coarse structural nested mean models are used to estimate treatment effects from longitudinal observational data. Coarse structural nested mean models lead to a large class of estimators. It turns out that estimates and standard errors may differ con
This paper focuses on the time series generated by the event counts of stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, existing methods of estimation are not applica
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