서베이앤헬스폴리시리서치센터

Kim, S. W., Heeringa, S. G., and Solenberger, P. W. (2004). “Inclusion probability proportional to size sampling: a nonlinear programming approach to ensure a nonnegative and stable variance estimator,” in Proceedings of the Survey Research Methods Section, American Statistical Association, 3821-3828, Toronto, Canada: Joint Statistical Meetings.

Abstract

Sample designs that use inclusion probability proportional to size sampling (IPPS) should have certain desirable properties including non-negativity and stability of the Sen-Yates-Grundy (1953) variance estimator. Jessen (1969) proposes several sampling schemes that partially achieve these desired properties by exerting controls over the joint probabilities that influence the variance estimator. Following his work, Nigam, Kumar and Gupta (1984) present a selection method that satisfactorily provides these properties, but their method involves considerable trial and error in the construction of binary incomplete block designs. In this paper, we introduce several new sampling schemes based on nonlinear programming. These methods are easily implemented and not only assure the non-negativity of the variance estimate but they are also flexible concerning stability of the variance estimator. Some of them are closely related to the approach developed by Kim, Heeringa, and Solenberger (2003). We demonstrate the usefulness and practicability of the new methods by applying them to example problems from the literature.

Key Words: Sen-Yates-Grundy Variance Estimator, Second-order Inclusion Probabilities, Binary Block Designs, Nonlinear Programming