Title: Generalised classes of estimators for population mean of sensitive variable using non-sensitive auxiliary parameters

Authors: S.K. Yadav; Amit Kumar Misra; Tarushree Bari

Addresses: Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, U.P., India ' Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, U.P., India ' Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, U.P., India

Abstract: Sousa et al. (2010) suggested transformed ratio type estimators for estimating the population mean of a sensitive variable in presence of some known population coefficients of a non-sensitive supplementary variable. In this article, we generalise the Sousa et al. (2010) family of estimators using some new population parameters of auxiliary information based on a randomised response technique (RRT). Further, we introduce a new efficient family of estimators for estimating the population mean of sensitivity variable using the approach given in Searls (1964) in the presence of the auxiliary information. The optimal value of Searl's constant is obtained using Lagrange's method of maxima-minima. Theoretical results are supported with a numerical illustration based on real datasets. In addition, a simulation study is carried out to compare the performances of the suggested and competing families of estimators. The estimator with good sampling properties and a lower mean square error (MSE) is recommended for various fields of applications of sensitive research.

Keywords: sensitive variable; scrambled response; randomised response technique; ratio type estimator; simple random sampling; simulation.

DOI: 10.1504/IJMMNO.2022.123964

International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.3, pp.287 - 302

Received: 09 Nov 2021
Accepted: 30 Jan 2022
Published online: 05 Jul 2022 *

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