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<p>In many production and agricultural surveys, obtaining accurate auxiliary information at the initial stage of sampling is often expensive or infeasible. Stratified double sampling offers a practical and cost-effective solution by selecting a large first-phase sample to collect inexpensive auxiliary data, followed by a smaller second-phase sample to observe the main study variable. In this study, a new estimator and a family of improved estimators for the population mean are proposed under a stratified double sampling framework. The proposed class includes modified ratio, product, regression, and exponential-type estimators that efficiently utilize first-phase auxiliary information, stratum-specific characteristics, and optimally determined weights. Analytical expressions for bias and mean squared error (MSE) are derived up to the first-order approximation, and the optimal constants are obtained by minimizing the MSE. Theoretical and empirical results demonstrate that the proposed estimators achieve lower MSE and higher percentage relative efficiency (PRE) compared to several existing estimators. A practical application is illustrated in agricultural yield estimation, where satellite-based vegetation indices are used as auxiliary information in the first phase, while crop-cutting experiments are conducted on a smaller subsample. This approach substantially reduces survey cost while improving the precision and timeliness of production estimates.</p>

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A new estimation strategy for the population mean under stratified double sampling: an empirical study based on production and productivity data

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Mukesh Kumar Verma,
  • Rahul Varshney,
  • Subhash Kumar Yadav,
  • Sarthak Sachdeva

摘要

In many production and agricultural surveys, obtaining accurate auxiliary information at the initial stage of sampling is often expensive or infeasible. Stratified double sampling offers a practical and cost-effective solution by selecting a large first-phase sample to collect inexpensive auxiliary data, followed by a smaller second-phase sample to observe the main study variable. In this study, a new estimator and a family of improved estimators for the population mean are proposed under a stratified double sampling framework. The proposed class includes modified ratio, product, regression, and exponential-type estimators that efficiently utilize first-phase auxiliary information, stratum-specific characteristics, and optimally determined weights. Analytical expressions for bias and mean squared error (MSE) are derived up to the first-order approximation, and the optimal constants are obtained by minimizing the MSE. Theoretical and empirical results demonstrate that the proposed estimators achieve lower MSE and higher percentage relative efficiency (PRE) compared to several existing estimators. A practical application is illustrated in agricultural yield estimation, where satellite-based vegetation indices are used as auxiliary information in the first phase, while crop-cutting experiments are conducted on a smaller subsample. This approach substantially reduces survey cost while improving the precision and timeliness of production estimates.