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Biometrika 1991 78(2):409-419; doi:10.1093/biomet/78.2.409
© 1991 by Biometrika Trust
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Poststratification using regression estimators when information on strata means and sizes is missing

DANNY PFEFFERMANN1 and ABBA M. KRIEGER2

1Department of Statistics, Hebrew University Jerusalem 91905, Israel
2Department of Statistics, University of Pennsylvania Philadelphia, Pennsylvania 19104, U. S.A.

Poststratification is often used to increase the precision of survey estimators. When applied to regression estimators, it assumes that the regression relationships in the various strata are different. This gives rise to the use of the separate regression estimator. In this paper, we consider situations where the strata affiliation of the population units is not specified in the frame so that the separate regression estimator is not available, the strata means of the regressor variable and the strata sizes being unknown. We propose a new regression type estimator which accounts for the different regression relationships in the various strata, but no longer depends on the unknown strata means and sizes. We show that this estimator is more precise than estimators that ignore the differences in the regression relationships. The theoretical comparisons are illustrated by simulation results.

Key Words: Design distribution • Histogram estimator • Separate regression estimator


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