On Variance Estimation for Model versus Design cum Model Unbiased Prediction in a Stratified Cluster Regression Setup
摘要
In this paper we consider a stratified clusters based finite population and develop a design cum model unbiased (DCMU) predictor for the finite population total using the two-stage cluster samples based survey data. The same design cum model based principle is applied to develop a valid variance function for the predictor and its unbiased estimate for the purpose of confidence intervals construction when needed. As far as the existing studies using a model unbiased prediction approach are concerned, unlike their claims, we demonstrate in this paper that the ordinary and/or generalized least square estimates computed conditionally on the given sample can never be model unbiased (MU) for the regression parameters involved in the prediction function which makes the existing MU prediction a flawed approach. Turning back to the design cum model unbiased predictions, while the aforementioned ordinary least square estimators in an independence setup can be used for DCMU prediction, the generalized least square estimators under a correlation setup are DCM biased and they are useless for any DCMU predictions. We, instead, use a doubly weighted (accommodating both sampling and inverse correlation weights) regression estimator which is DCMU for the parameter leading to DCMU predictions. The variance of the doubly weighted estimator based predictor and its unbiased estimates are provided by exploiting the DCM based approach. As the clusters based survey data are frequently encountered in general by statistical agencies, the proposed methodological study should be highly beneficial to those practitioners among other applied statistics researchers.