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<p>In a clusters based finite population (FP) setup, the estimation/prediction of the FP total parameter using a complex such as two-stage cluster sample has been a core problem of interest over the last five decades. In general a super-population model based prediction approach is used for such an estimation. The inference properties such as variance of the predictor and its unbiased estimation are also studied. However as the existing model based prediction approach primarily estimates the prediction function by fitting the super-population model directly to the sampled data, it produces a biased and hence an invalid predictor because of ignoring the finite population as the source of the sample in the estimation process. As a remedy, Sutradhar (<CitationRef CitationID="CR23">2024b</CitationRef>, <i>Sankhya A, 951-991</i>) has outlined a design cum model (DCM) based prediction approach which produces a DCM unbiased (DCMU) predictor for the finite population total parameter. In this paper, we demonstrate how one can exploit this DCM based approach and compute an exact variance for the proposed DCMU total predictor. We also develop an unbiased variance estimator which can be used for confidence intervals construction when needed or for variance based efficiency comparison with other possible predictors.</p>

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Prediction Variance and Its Unbiased Estimation Challenge in a Two-stage Cluster Sampling Setup

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Brajendra C. Sutradhar

摘要

In a clusters based finite population (FP) setup, the estimation/prediction of the FP total parameter using a complex such as two-stage cluster sample has been a core problem of interest over the last five decades. In general a super-population model based prediction approach is used for such an estimation. The inference properties such as variance of the predictor and its unbiased estimation are also studied. However as the existing model based prediction approach primarily estimates the prediction function by fitting the super-population model directly to the sampled data, it produces a biased and hence an invalid predictor because of ignoring the finite population as the source of the sample in the estimation process. As a remedy, Sutradhar (2024b, Sankhya A, 951-991) has outlined a design cum model (DCM) based prediction approach which produces a DCM unbiased (DCMU) predictor for the finite population total parameter. In this paper, we demonstrate how one can exploit this DCM based approach and compute an exact variance for the proposed DCMU total predictor. We also develop an unbiased variance estimator which can be used for confidence intervals construction when needed or for variance based efficiency comparison with other possible predictors.