Abstract
In this paper, a general class of estimators is proposed for estimating the finite population mean for sensitive variable, in the presence of measurement error and non-response in simple random sampling. Expressions for bias and mean square error up to first order of approximation, are derived. Impact of measurement errors is examined using real data sets, including the survey conducted at Quaid-i-Azam University, Islamabad. Simulated data sets are also used to observe the performance of the proposed estimators in comparison to some other estimators. We obtain the empirical bias and MSE values for the proposed and the competing estimators.
Highlights
If the variable of interest is sensitive in nature, the chance to get incorrect information increases
The problem of measurement error is usually ignored during the sensitive surveys and the assumption is made that the information obtained is free from error
We have proposed a class of estimators for the population mean of a sensitive variable in the presence of measurement error and non-response simultaneously, under simple random sampling
Summary
If the variable of interest is sensitive in nature, the chance to get incorrect information increases. For estimation of mean of a sensitive quantitative variable, the Randomized Response Model (RRM) was used by [10] and [11]. Further work in this are done by [12–21], among others. We have proposed a class of estimators for the population mean of a sensitive variable in the presence of measurement error and non-response simultaneously, under simple random sampling. Let S2Q, S2V and S2T be the population variances associated with measurement error in the variables. S2 Tð2Þ population variances associated with measurement error in the variables Z, X and Rx respectively for the nonresponding units.
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