An Analysis of the Properties of a Newly Proposed Non‑Randomised Response Technique

Barbara Kowalczyk

doi:10.18778/0208-6018.358.01

Authors

Barbara Kowalczyk SGH Warsaw School of Economics, Collegium of Economic Analysis Institute of Econometrics, Mathematical Statistics Unit, Warsaw, Poland https://orcid.org/0000-0002-5407-3438

DOI:

https://doi.org/10.18778/0208-6018.358.01

Keywords:

indirect questioning, sensitive questions, non‑randomised response techniques, crosswise model, ML estimation, degree of privacy protection

Abstract

Non‑randomised response (NRR) techniques are modern and constantly evolving methods intended for dealing with sensitive topics in surveys, such as tax evasion, black market, corruption etc. The paper introduces a new NRR technique that can be seen as a generalisation of the well‑known crosswise model (CM). In the paper, methodology of the new generalised crosswise model (GCM) is presented and the maximum likelihood estimator of the unknown population sensitive proportion is obtained. Also, the problem of privacy protection is discussed. The properties of the newly proposed GCM are examined. Then the GCM is compared with the traditional CM. The paper shows that mathematically the CM is a special case of the newly proposed generalised CM and that this generalisation has high practical relevance.

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