, Volume 76, Issue 2, pp 203–230 | Cite as

Dealing sensitive characters on successive occasions through a general class of estimators using scrambled response techniques

  • Kumari PriyankaEmail author
  • Pidugu Trisandhya
  • Richa Mittal


Present article endeavours to propose a general class of estimators to estimate population mean of a sensitive character using non-sensitive auxiliary information under five different scrambled response models in two occasions successive sampling. Various well-known estimators have been modified for the estimation of sensitive population mean and hence they also become a member of proposed general class of estimators. Properties of proposed class of estimators have been derived and checked empirically while comparing the proposed class of estimators with respect to modified Jessen (Iowa Agric Exp Stn Res Bull 304:1–104, 1942) type estimator and modified Singh (Stat Transit 7(1):21–26, 2005) type estimator under five different scrambled response models. The effectiveness of different models has been discussed while comparing it with the direct questioning methods. A model for optimum total cost has also been proposed. Privacy protection has been elaborated for all considered models. Numerical illustrations including simulation studies are abundant to the theoretical results. Finally suitable recommendations are forwarded.


Successive sampling Scrambled response model Sensitive character Class of estimators Population mean Bias Mean squared error Optimum replacement policy 

Mathematics Subject Classification




The authors wish to thank anonymous reviewer and Professor Giovanni Maria Giorgi, Editor in Chief for their careful reading and constructive suggestions which lead to improvement over an earlier version of the paper.


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Copyright information

© Sapienza Università di Roma 2017

Authors and Affiliations

  • Kumari Priyanka
    • 1
    Email author
  • Pidugu Trisandhya
    • 1
  • Richa Mittal
    • 2
  1. 1.Department of Mathematics, Shivaji CollegeUniversity of DelhiNew DelhiIndia
  2. 2.Department of MathematicsNIT CalicutCalicutIndia

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