Joint influence of measurement errors and randomized response technique on mean estimation under stratified double sampling

Ronald Onyango,Francis Odundo,Brian Oduor

doi:10.30538/oms2021.0156

Abstract

The present study proposes a generalized mean estimator for a sensitive variable using a non-sensitive auxiliary variable in the presence of measurement errors based on the Randomized Response Technique (RRT). Expressions for the bias and mean squared error for the proposed estimator are correctly derived up to the first order of approximation. Furthermore, the optimum conditions and minimum mean squared error for the proposed estimator are determined. The efficiency of the proposed estimator is studied both theoretically and numerically using simulated and real data sets. The numerical study reveals that the use of the Randomized Response Technique (RRT) in a survey contaminated with measurement errors increases the variances and mean squared errors of estimators of the finite population mean.

Highlights

A uxiliary variables are closely related to the survey variable and are used in a survey at the design and estimation stage to improve the efficiency of estimators of the finite population mean
In the Randomized Response Technique (RRT), a scrambled variable that is independent of the survey and auxiliary variables are used in the estimation of the finite population means of a sensitive variable
The proposed strategy is useful for the construction of accurate confidence intervals for unknown population parameters in a survey based on the Randomized Response Technique (RRT) and contaminated with measurement errors

Summary

Introduction

A numerical study is conducted using both simulated and real data sets to compare the performance of the proposed estimator with some existing estimators in the literature. The real data set is obtained from Sarndal et al, [18]. Scrambling responses that are normally distributed, Shi ∼ N (0, 2) is generated for each unit in the data set. Thereafter, the response variable is obtained as Zhi = Yhi + Shi. normally distributed measurement errors with mean 2 and variance 5 are introduced to each unit of the response and auxiliary variables. The efficiency of the proposed estimator is compared with other estimators using the minimum variance and the Percent Relative Efficiency (PRE) approaches. The Percent Relative Efficiency (PRE) of the estimators are obtained using the expression; PRE = Var(t0) × 100,.

Population description and notations

Proposed estimator

Xh Xh 8 Xh X1h

Members of family of Proposed generalized estimator

Discussion

Conclusion