<p>Estimating the population parameter is a fundamental problem in survey sampling, particularly when full population data is unavailable. While traditional estimators typically utilize quantitative auxiliary variables to enhance efficiency, the use of qualitative or binary auxiliary information such as “presence or absence” remains a relatively less explored area, especially for mean estimation. This study develops a generalized class of estimators for the population mean by incorporating such auxiliary attributes in binary form. In particular, we propose a memory-type estimator based on the exponentially weighted moving average (EWMA) statistic, which effectively incorporates historical sample information to improve estimator performance. Theoretical expressions for bias and mean squared error (MSE) are derived, and several specific forms of the proposed estimators are examined. The efficiency of these estimators is compared with traditional ratio, product, exponential and regression estimators. Empirical and simulation studies demonstrate that the proposed estimators, including the EWMA-based memory-type estimator, consistently yield lower MSE, especially under varying sample sizes and correlations between the study variable and the auxiliary attribute. These findings highlight the practical value of using auxiliary attributes and memory-type strategies for improved mean estimation when quantitative auxiliary data is unavailable.</p>

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Harnessing qualitative data for precision in population mean estimation in time-scaled surveys

  • Prayas Sharma,
  • Poonam Singh,
  • Mamta Kumari,
  • Abhilasha,
  • Amit Kumar Misra

摘要

Estimating the population parameter is a fundamental problem in survey sampling, particularly when full population data is unavailable. While traditional estimators typically utilize quantitative auxiliary variables to enhance efficiency, the use of qualitative or binary auxiliary information such as “presence or absence” remains a relatively less explored area, especially for mean estimation. This study develops a generalized class of estimators for the population mean by incorporating such auxiliary attributes in binary form. In particular, we propose a memory-type estimator based on the exponentially weighted moving average (EWMA) statistic, which effectively incorporates historical sample information to improve estimator performance. Theoretical expressions for bias and mean squared error (MSE) are derived, and several specific forms of the proposed estimators are examined. The efficiency of these estimators is compared with traditional ratio, product, exponential and regression estimators. Empirical and simulation studies demonstrate that the proposed estimators, including the EWMA-based memory-type estimator, consistently yield lower MSE, especially under varying sample sizes and correlations between the study variable and the auxiliary attribute. These findings highlight the practical value of using auxiliary attributes and memory-type strategies for improved mean estimation when quantitative auxiliary data is unavailable.