Properties of Some Sample Designs Based on Imperfect Frame Information

Randall K. Powers and John L. Eltinge


Large-scale sample designs generally use auxiliary information obtained through frames or other data sources. In some cases, limitations on this information may reduce the efficiency of the resulting sample design. For example, in designs that base selection probabilities on measures of unit size, the size measures may be subject to measurement errors, or may be unavailable for some population units. For such cases, one may view standard “probability proportional to size“ designs as approximations to nominally optimal designs that could be produced if one knew the mean function, E( Y | Z ), and variance function, V( Y | Z ), of a survey variable Y, conditional on auxiliary data Z, which may include the imperfect size measures. Properties of the resulting designs will depend on (1) the precision with which E( Y | Z ) and V( Y | Z ) are known; (2) the extent to which these conditional moments display similar patterns across different survey variables Y; and (3) information on (1) and (2) provided through preliminary empirical studies. Following a brief review of some theory and literature, this paper explores issues (1), (2) and (3) through a detailed simulation study.