Abstract
AbstractA system of predictors for estimating a finite population variance is defined and shown to be asymptotically design‐unbiased (ADU) and asymptotically design‐consistent (ADC) under probability sampling. An asymptotic mean squared error (MSE) of a generalized regression‐type predictor, generated from the system, is obtained. The suggested predictor attains the minimum expected variance of any design‐unbiased estimator when the superpopulation model is correct. The generalized regression‐type predictor and the predictor suggested by Mukhopadhyay (1990) are compared.
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