Conditioning post-stratified inference following two-stage, equal-probability sampling. Gregoire, T. G., Ringvall, A. H., Ståhl, G., & Næsset, E. Environmental and Ecological Statistics, 23(1):141-154, 2016.
Conditioning post-stratified inference following two-stage, equal-probability sampling [link]Paper  doi  abstract   bibtex   
This paper considers conditioning on the size of the samples observed in post-strata following a two-stage sampling design. We argue that it is reasonable to do so despite the complexity of the design. We derive an expression for the covariances among post-strata estimates resulting from secondary sampling units on the same primary sampling unit which reside in different post-strata. To motivate both issues we describe a two-stage LiDAR-assisted sample for aboveground biomass that was reported in Gregoire et al. (Can J For Res 41:83–95, 2011).
@article{RN475,
   author = {Gregoire, Timothy G. and Ringvall, Anna H. and Ståhl, Göran and Næsset, Erik},
   title = {Conditioning post-stratified inference following two-stage, equal-probability sampling},
   journal = {Environmental and Ecological Statistics},
   volume = {23},
   number = {1},
   pages = {141-154},
   abstract = {This paper considers conditioning on the size of the samples observed in post-strata following a two-stage sampling design. We argue that it is reasonable to do so despite the complexity of the design. We derive an expression for the covariances among post-strata estimates resulting from secondary sampling units on the same primary sampling unit which reside in different post-strata. To motivate both issues we describe a two-stage LiDAR-assisted sample for aboveground biomass that was reported in Gregoire et al. (Can J For Res 41:83–95, 2011).},
   ISSN = {1573-3009},
   DOI = {10.1007/s10651-015-0332-9},
   url = {https://doi.org/10.1007/s10651-015-0332-9},
   year = {2016},
   type = {Journal Article}
}

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