Calibration estimator for a sensitive variable using dual auxiliary information under measurement errors

Zhiqiang Pang, Xijuan Niu, Zhaoxu Wang and Jingchen You

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 3, 864-881

Abstract: In survey research, it is commonly assumed that all the observations are measured accurately. However, in practice, this assumption is not achieved due to many reasons, so it causes measurement errors to be inevitably present in the sample estimation. This article addresses the problem of estimation of finite population mean under stratified random sampling in the presence of measurement errors. A calibration estimator is proposed for the sensitive variable by utilizing suitable calibration techniques, which can be applied to obtain the optimal strata weight. The calibration estimator not only incorporates the auxiliary information but also the ranks of the auxiliary variable. Expressions for bias and mean square error are derived up to first order of approximation. Simulation studies and real-life datasets are used to assess the performances of the proposed estimator by comparing them with the contemporary estimators in the presence and absence of measurement errors. The theoretical and empirical studies demonstrate that the proposed calibration estimator consistently outperforms classical mean, usual ratio, conventional difference, Khail randomized response estimators.

Date: 2025
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DOI: 10.1080/03610926.2024.2322617

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