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On the estimation of correlation coefficient using scrambled responses. (English) Zbl 1365.62052
Chaudhuri, Arijit (ed.) et al., Data gathering, analysis and protection of privacy through randomized response techniques: qualitative and quantitative human traits. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-63570-9/hbk; 978-0-444-63571-6/ebook). Handbook of Statistics 34, 43-90 (2016).
Summary: The problem of estimating the correlation coefficient using scrambled responses based on the B. H. Eichhorn and L. S. Hayre [J. Stat. Plan. Inference 7, 307–316 (1983)] model was considered by S. Singh, [“On improved strategies in survey sampling”, unpublished dissertation (1991)] who had studied the asymptotic behavior of the bias and variance expressions. As pointed out by A. Chaudhuri [Randomized response and indirect questioning techniques in surveys. Boca Raton, FL: CRC Press (2011; Zbl 1278.62001); D. R. Bellhouse, “Estimation of correlation in randomized response”, Surv. Methodol. 21, 13–19 (1995)] has considered the problem of estimating the correlation coefficient, but the details are cumbersome and are not reported in his monograph. Chaudhuri [loc. cit.] further indicates that efforts are needed to refine developments to estimate correlation coefficient to switch over to the utilization of procedures when only randomized response survey data are available. He mentioned that no literature of relevance seems available yet. In this chapter, an attempt has been made to answer the question raised by Chaudhuri [loc. cit].
For the entire collection see [Zbl 1349.62001].
MSC:
62D05 Sampling theory, sample surveys
62H20 Measures of association (correlation, canonical correlation, etc.)
94A62 Authentication, digital signatures and secret sharing
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