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<p>Improving efficiency in finite population parameter estimation becomes more crucial when the data are collected using the randomized response technique, as the incorporation of randomization mechanisms introduces additional variation in responses. This adds variability, which, in turn, inflates the variance of the resultant estimates. In this article, we explore the use of a superpopulation model that relates the study variable to one or more covariates to enhance estimation efficiency. A general linear prediction estimator for the finite population parameter, which is a linear combination of population values, is derived under the scrambled response model&#xa0;assuming the study variable is both sensitive and quantitative in nature, assuming the study variable is both sensitive and quantitative in nature. The model-based properties of this estimator, along with several of its special cases, are examined in detail. A simulation study is conducted to evaluate the estimators’ performance using design-based expected square prediction error (ESPE) and relative efficiency values. The proposed estimation approach is then applied to estimate the mean age at first sexual intercourse for women using data from the Pakistan Demographic Health Survey (PDHS 2017–2018), demonstrating its practical applicability. The findings underscore the effectiveness of the suggested estimation method for surveys involving sensitive quantitative variables. This study highlights its relevance in demographic health surveys, particularly in contexts where questions related to sexual behavior tend to yield higher rates of non-response.</p>

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Improving Efficiency of Finite Population Estimates Under Scrambled Response Models Using Auxiliary Information

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Shakeel Ahmed,
  • Javid Shabbir

摘要

Improving efficiency in finite population parameter estimation becomes more crucial when the data are collected using the randomized response technique, as the incorporation of randomization mechanisms introduces additional variation in responses. This adds variability, which, in turn, inflates the variance of the resultant estimates. In this article, we explore the use of a superpopulation model that relates the study variable to one or more covariates to enhance estimation efficiency. A general linear prediction estimator for the finite population parameter, which is a linear combination of population values, is derived under the scrambled response model assuming the study variable is both sensitive and quantitative in nature, assuming the study variable is both sensitive and quantitative in nature. The model-based properties of this estimator, along with several of its special cases, are examined in detail. A simulation study is conducted to evaluate the estimators’ performance using design-based expected square prediction error (ESPE) and relative efficiency values. The proposed estimation approach is then applied to estimate the mean age at first sexual intercourse for women using data from the Pakistan Demographic Health Survey (PDHS 2017–2018), demonstrating its practical applicability. The findings underscore the effectiveness of the suggested estimation method for surveys involving sensitive quantitative variables. This study highlights its relevance in demographic health surveys, particularly in contexts where questions related to sexual behavior tend to yield higher rates of non-response.