Sampling from overlapping subpopulations

Summary Statistical problems in connection with classified data, stratified sampling, cluster sampling and two-stage sampling may be formulated in terms of overlapping subpopulations instead of disjoint classes, strata, clusters or primary sampling units. The introduction in section 1 serves to unify the notation to be used and to exemplify the type of problems that are to be generalized. Samples where the units are classified into overlapping classes are studied in section 2. The applicability is illustrated with an estimation problem in connection with destructive tests. Section 3 treats sampling from overlapping strata and estimation of the sizes of the intersections. Section 4 discusses problems in conjunction with sampling of overlapping clusters. Graphs or networks representing populations with binary relationships are used to exemplify sampling of overlapping clusters. Section 5 is devoted to some examples of two-stage sampling where the primary sampling units are overlapping subsets.