Confidence Intervals for Sub‐Domain Parameters When the Sub‐Domain Sample Size is Random

Robert J. Casady, Alan H. Dorfman, and Suojin Wang


Let be a population sub-domain of interest and assume that the elements of A cannot be identified on the sampling frame and the number of elements in A is not known. Further assume that a sample of fixed size (say n) is selected from the entire frame and the resulting sub- domain sample size (say nA) is random. The problem addressed is the construction of a confidence interval for a sub-domain parameter such as the sub-domain aggregate TA = ä i xi . The usual approach to this problem is to redefine xi , by setting xi = 0 if i î A. Thus, the construction of a confidence interval for the sub-domain total is recast as the construction of a confidence interval for a population total which can be addressed (at least asymptotically in n) by normal theory. As an alternative, we condition on and construct confidence intervals which have approximately nominal coverage under certain assumptions regarding the sub-domain population. We evaluate the new approach empirically using data from the BLS Occupational Compensation Survey.