Engineering and Applied Science Letter
Vol. 6 (2023), Issue 1, pp. 37 – 48
ISSN: 2617-9709 (Online) 2617-9695 (Print)
DOI: 10.30538/psrp-easl2023.0094
Estimation of finite population mean of a sensitive variable using three-stage orrt in the presence of non-response and measurement errors
Ronald Onyango\(^{1,*}\), Samuel B. Apima\(^2\) and Amos Wanjara\(^2\)
\(^{1}\) Department of Applied Statistics, Financial Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, Kenya
\(^{2}\) Department of Mathematics and Statistics, Kaimosi Friends University, Kenya
Copyright © 2023 Ronald Onyango, Samuel B. Apima and Amos Wanjara. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 06, 2023 – Accepted: June 20, 2023 – Published: June 30, 2023
Abstract
The purpose of this study is to present a generalized class of estimators using the three-stage Optional Randomized Response Technique (ORRT) in the presence of non-response and measurement errors on a sensitive study variable. The proposed estimator makes use of dual auxiliary information. The expression for the bias and mean square error of the proposed estimator are derived using Taylor series expansion. The proposed estimator’s applicability is proven using real data sets. A numerical study is used to compare the efficiency of the proposed estimator with adapted estimators of the finite population mean. The suggested estimator performs better than adapted ordinary, ratio, and exponential ratio-type estimators in the presence of both non-response and measurement errors. The efficiency of the proposed estimator of population mean declines as the inverse sampling rate, non-response rate, and sensitivity level of the survey question increase.
Keywords:
Sensitivity level; non-response; measurement errors; bias; efficiency