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Biometrika 1987 74(1):216-219; doi:10.1093/biomet/74.1.216
© 1987 by Biometrika Trust
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MISCELLANEA

The effect of changes of location on least-squares estimators for samples stratified on the dependent variable

GILLIAN M. RAAB and YU JING ZHOU

Medical Statistics Unit, University of Edinburgh, Medical School Teviot Place, Edinburgh EH8 9AG, U.K.
Department of Biostatistics, Graduate School of Public Health Pittsburgh, Pennsylvania 15261, U.S.A.

The consistent least-squares estimator, proposed by Jewell (1985) for linear regression with data arising from stratified samples, lacks invariance with respect to a change of location of the dependent variable. Simulation suggests that its efficiency is reduced when the origin of the dependent variable is far from its mean. This estimator can be made invariant to a change of location by specifying that the dependent variable is measured from the estimated population mean. Another similar invariant estimator is also suggested.

Key Words: Invariance • Least-squares • Linear regression • Maximum likelihood • Stratified sampling


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