Robust-regression-type estimators for improving mean estimation of sensitive variables by using auxiliary information

Abstract

In case of sensitive research, estimation of mean is a major concern in survey studies and regression estimators utilizing traditional regression coefficient are the most favored choices for it. Recently, Zaman and Bulut [2018 Zaman, T., and H. Bulut. 2018. Modified ratio estimators using robust regression methods. Communications in Statistics - Theory and Methods 48:2039–48. doi: 10.1080/03610926.2018.1441419.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]. Modified ratio estimators using robust regression methods. Communications in Statistics - Theory and Methods, DOI:10.1080/03610926.2018.1441419] have developed a class of ratio-type estimators for the mean estimation of non-sensitive variable utilizing robust regression coefficients. In this paper, we have generalized their family of estimators to the case where the study variable refers to sensitive issues which produces measurement errors due to non-responses and/or untruthful reporting. These errors may be reduced by enhancing respondent cooperation through scrambled response methods that mask the true value of the sensitive variable. Hence, two scrambled response models Pollock and Bek (1976 Pollock, K. H., and Y. Bek. 1976. A comparison of three randomized response models for quantitative data. Journal of the American Statistical Association 71 (356):884–6. doi: 10.1080/01621459.1976.10480963.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Bar-Lev, Bobovitch, and Boukai (2004 Bar-Lev, S. K., E. Bobovitch, and B. Boukai. 2004. A note on randomized response models for quantitative data. Metrika 60 (3):255–60. doi: 10.1007/s001840300308.[Crossref], [Web of Science ®] , [Google Scholar]) are discussed for the purposes of this article. We have also developed a class of robust-regression type estimators in case of sensitive research. Some estimators belonging to the class are shown and the mean square errors are determined. Theoretical and empirical illustration is done through real and artificial data sets for assessing the performance of adapted and proposed class.