Estimating the First Selected PSU Mean in a Two Stage Cluster Sample- Expanding the PSUs

نویسنده

  • Ed Stanek
چکیده

Scott and Smith (1969) develop estimators for linear functions from a two stage cluster sample, with their discussion repeated in many places. This discussion was reviewed in c01ed13.doc. It is note-worthy that Scott and Smith allow expressions for the variance to depend on the cluster. A similar development is given by Vallient et al.. We repeated the derivation of Vallient et al using the finite population variance in c01ed15.doc. These results were extended to settings with response error in c01ed25.doc. Both sets of results assume that the number of SSUs in a PSU is equal for all PSUs. In addition, both derivations are based on a ‘collapsed’ version of a vector of random variables, similar to the vector of random variables usually considered. In an additional document, the expected value and variance is developed for a two stage problem with unequal size PSUs (see c01ed26.doc). However, this development stops short of estimation. In order to clearly construct the estimating equations, the un-balance in PSU sizes has to be accounted for. It seems that this accounting will be more straightforward in an expanded population framework. With this in mind, we repeat the development of balanced two stage sampling in an expanded population framework. We consider here the simpler setting where we have equal size PSUs, and no response error. We expand the representation of the PSUs, but not of the SSUs. Our goal is provide a model for completing the development of the two stage estimator with unequal PSU sizes.

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تاریخ انتشار 2001