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Abstract:
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Auxiliary variables are extensively used in survey sampling to construct Generalized Regression (GR) estimators, or Optimal Regression (OR) estimators, of totals and means. These estimators are also calibration estimators, reproducing for the auxiliary variables the estimated parameters when the latter are available from external sources. This paper explores the possibility of improving the efficiency of such estimators when the utilized auxiliary variables are continuous, by augmenting the set of these variables with selected exponents of them. It is shown for the case of a single continuous auxiliary variable and simple random sampling or stratified simple random sampling, that the addition of a fractional exponent of the auxiliary variable improves the efficiency of the OR estimator to the degree of the implied increase of the coefficient of determination for the study variables. A simulation study shows that this additional variable improves the efficiency of the GR estimator greatly, even when the coefficient of determination is not increased.
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