Shrinkage Estimation Procedure of Population Mean with Stigmatizing Character in Unrelated Question Randomized Response
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RESEARCH ARTICLE
Shrinkage Estimation Procedure of Population Mean with Stigmatizing Character in Unrelated Question Randomized Response Technique G. N. Singh1 • Surbhi Suman1
Received: 5 March 2016 / Revised: 27 August 2018 / Accepted: 20 December 2018 The National Academy of Sciences, India 2019
Abstract This work deals with the estimation of population mean related to sensitive characteristic. A shrinkage estimator of population mean using a prior information is proposed under unrelated question randomized response model where one of the two questions presented to the respondents is non-stigmatized and unrelated to the stigmatized character. The properties of proposed estimator have been discussed, and empirical studies are accomplished to demonstrate the performance of the proposed estimation procedure. Keywords Bias Mean square error Guessed value Randomized response model
one month?’’ and Y: ‘‘How much did you spend on buying stationery during the last 1 month?’’ Since the second question relates to an innocuous characteristic that is unrelated to the expenditure over cigarettes, one can reasonably expect that the respondent’s privacy is being sufficiently well protected. The uncorrelated question model for quantitative variable was further analyzed and reformed by Umesh and Paterson [4], Pollock and Bek [5], Eichhorn and Hayre [6], Gupta and Shabbir [7], Shaul et al. [8], Gupta et al. [7], Saha [9] and Dinna and Perri [10] among others. Motivated with the above works, we suggest a modified estimator of population mean of sensitive characteristics which utilizes its guessed or prior value available from the past studies.
1 Introduction Randomized response survey techniques are widely used by survey practitioners to eliminate evasive answers for the questions related to the sensitive issues. This technique was initially suggested by Warner [1] and further supplemented by Greenberg et al. [2] where the authors have proposed an unrelated question randomized response model to estimate the population proportion of persons having the sensitive characteristic. Further Greenberg et al. [3] suggested an extension of the unrelated question model to the quantitative character. For example, the sensitive question may be X: ‘‘How much did you spend on cigarettes over the last
& Surbhi Suman [email protected] 1
Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
2 Review of Uncorrelated Quantitative Randomized Response Model for Stigmatized Characteristic The uncorrelated randomized response model was suggested by Greenberg et al. [3] for quantitative characteristics. He considered a sensitive characteristic X and nonsensitive characteristic Y which are continuous with probability density functions g(x) and h(y), respectively. To estimate the population mean lX of the sensitive characteristic X, when the population mean of non-sensitive characteristic Y is known, a sample of size n has been drawn from the population using sampling scheme simp
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