Estimation of domain means using two-phase sampling

Abstract

SUMMARY In sample surveys, it is often desired to estimate the means of subpopulations or ‘domains of study’. If there is no list of the units comprising each domain, a two-phase sampling procedure may be employed. One possibility is to select a simple random sample of size n ′ with the domain to which each unit belongs being determined. Then a simple random subsample of size n′ j , is selected from the n′ j , units found in the first phase sample to be members of the j th domain. Given the values of the n′ j , it is desired to allocate a fixed total second phase sample size, n , to the domains in an optimal manner. Then one may determine the optimal choices for n′ and n . Alternatively, one may use a stratified random sample of size n' with n' h units being selected from the h th stratum. Given that the first phase sample yields n′ hj units in the h th stratum, j th domain, the number of units, n hj , to be subsampled by simple random sampling is to be determined to maximize a measure of precision.