Asymptotic properties of cross‐classified sampling designs

Abstract We investigate the family of cross‐classified sampling designs across an arbitrary number of dimensions. We introduce a variance decomposition that enables the derivation of general asymptotic properties for these designs and the development of straightforward and asymptotically unbiased variance estimators. Additionally, we demonstrate the suitability of weighted bootstrap techniques for cross‐classified sampling, given the availability of a weighted bootstrap technique in each dimension. Our conclusions are supported by an extensive simulation study. Finally, we apply the proposed methods to a French longitudinal survey conducted on children.