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<p>This paper deals with an optimal finite population (FP) total prediction in a regression setup using a survey sample (SS) taken from the FP based on a suitable sampling design. As far as the FP structure is concerned, both independent and correlation setups are considered, in the later case FP elements are assumed to be pairwise correlated. Also it is assumed that the covariates in a FP are known possibly from a sampling frame. In a model based prediction approach it is standard to assume a super-population (SP) regression model for the FP based hypothetical data so that the non-sampled response total involved in the prediction function may be predicted by its SP model based expectation involving unknown regression parameters requiring their optimal estimation. For the purpose, the decades long existing studies have estimated these SP parameters based on the SS using the so-called conditional (on the SS) MUOLS (model unbiased ordinary least square) estimators in the independent setup and similarly conditional MUGLS (model unbiased generalized least square) estimators in the correlation setup. However, as it is demonstrated in the paper, because the covariates are likely to vary from one sample to another, a SS in the present FP setup is subject to randomness due to both sampling variation and model errors. Thus, it is a major mistake to claim that the OLS and GLS estimators are model unbiased (MU) for the SP regression parameters and hence they can never produce MU prediction. In contrary, when both sampling variation and model errors are accommodated appropriately, the OLS estimator may be shown to be a design cum model unbiased (DCMU) estimator under the independence setup, but the GLS estimator is neither DU nor DCMU, leave alone its MU property. As a remedy, following some recent studies we propose a DblyW (doubly weighted) estimator which is DU producing DCMU estimation and prediction as well. We then exploit this new DCMU estimation approach to compute the exact variance for the total predictors both under independence and correlation setups.</p>

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Model versus Design cum Model Unbiased Predictions for Finite Population Total Under Both Independent and Correlation Setups: An Appraisal

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Brajendra C. Sutradhar

摘要

This paper deals with an optimal finite population (FP) total prediction in a regression setup using a survey sample (SS) taken from the FP based on a suitable sampling design. As far as the FP structure is concerned, both independent and correlation setups are considered, in the later case FP elements are assumed to be pairwise correlated. Also it is assumed that the covariates in a FP are known possibly from a sampling frame. In a model based prediction approach it is standard to assume a super-population (SP) regression model for the FP based hypothetical data so that the non-sampled response total involved in the prediction function may be predicted by its SP model based expectation involving unknown regression parameters requiring their optimal estimation. For the purpose, the decades long existing studies have estimated these SP parameters based on the SS using the so-called conditional (on the SS) MUOLS (model unbiased ordinary least square) estimators in the independent setup and similarly conditional MUGLS (model unbiased generalized least square) estimators in the correlation setup. However, as it is demonstrated in the paper, because the covariates are likely to vary from one sample to another, a SS in the present FP setup is subject to randomness due to both sampling variation and model errors. Thus, it is a major mistake to claim that the OLS and GLS estimators are model unbiased (MU) for the SP regression parameters and hence they can never produce MU prediction. In contrary, when both sampling variation and model errors are accommodated appropriately, the OLS estimator may be shown to be a design cum model unbiased (DCMU) estimator under the independence setup, but the GLS estimator is neither DU nor DCMU, leave alone its MU property. As a remedy, following some recent studies we propose a DblyW (doubly weighted) estimator which is DU producing DCMU estimation and prediction as well. We then exploit this new DCMU estimation approach to compute the exact variance for the total predictors both under independence and correlation setups.