Variance Estimation for a Specified Multiple-Frame Survey Design

This paper is concerned with the estimation of the variance of estimates based on a multiple-frame sample design in which alphabetic clusters of elements have been sampled from different lists, and where elements selected from different lists may correspond to the same element of the population of interest. A nesting procedure is used to assure that clusters selected from any one of the lists are also in the sample for any other list in which an equal or greater sampling rate has been specified.