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Robustness of some sampling strategies under polynomial regression models. (English) Zbl 0829.62015

Summary: It is well-known that under a class of superpopulation models with the relationship between the expected value of the main variable \(y'\) and the auxiliary variable \(x\) being a straight line passing through the origin, the strategies \((\pi p s\), HTE), Hansen-Hurwitz stragety, Rao-Hartley- Cochran strategy and Midzuno strategy are all model-unbiased with \((\pi ps\), HTE) attaining the lower bound of average variance of unbiased estimators. An attempt has been made in this paper to study the robustness of these strategies (in the average mean square error sense) with respect to the departure of this model towards the general polynomial regression models.

MSC:

62D05 Sampling theory, sample surveys
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