Confidence intervals for domain parameters when the domain sample size is random - ARCHIVED

Let A be a population 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 domain sample size (say n_A) is random. The problem addressed is the construction of a confidence interval for a domain parameter such as the domain aggregate T_A = \sum_{i \in A} x_i. The usual approach to this problem is to redefine x_i, by setting x_i = 0 if i \notin A. Thus, the construction of a confidence interval for the 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 n_A and construct confidence intervals which have approximately nominal coverage under certain assumptions regarding the domain population. We evaluate the new approach empirically using artificial populations and data from the Bureau of Labor Statistics (BLS) Occupational Compensation Survey.