Estimation of the mean of a sensitive variable in the presence of auxiliary information

Sat Gupta, Javid Shabbir, Rita Sousa, Pedro Corte-Real

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


Sousa et al. (2010) introduced a ratio estimator for the mean of a sensitive variable and showed that this estimator performs better than the ordinary mean estimator based on a randomized response technique (RRT). In this article, we introduce a regression estimator that performs better than the ratio estimator even for modest correlation between the primary and the auxiliary variables. The underlying assumption is that the primary variable is sensitive in nature but a non sensitive auxiliary variable exists that is positively correlated with the primary variable. Expressions for the Bias and MSE (Mean Square Error) are derived based on the first order of approximation. It is shown that the proposed regression estimator performs better than the ratio estimator and the ordinary RRT mean estimator (that does not utilize the auxiliary information). We also consider a generalized regression-cum-ratio estimator that has even smaller MSE. An extensive simulation study is presented to evaluate the performances of the proposed estimators in relation to other estimators in the study. The procedure is also applied to some financial data: purchase orders (a sensitive variable) and gross turnover (a non sensitive variable) in 2009 for a population of 5,336 companies in Portugal from a survey on Information and Communication Technologies (ICT) usage.

Original languageEnglish
Pages (from-to)2394-2404
Number of pages11
JournalCommunications in Statistics - Theory and Methods
Issue number13-14(SI)
Publication statusPublished - 1 Jul 2012


  • Absolute relative bias
  • Mean square error
  • Randomized response technique
  • Regression estimator
  • Regression-cum-ratio estimator


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