On an indirect response model. (English) Zbl 1365.62043

Padmawar, V. R.

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, 497-513 (2016).

Summary: It is now pant of folklore that when the statistician has to collect data on characteristics that are either too personal, sensitive, or stigmatizing; randomized response (RR) techniques are used. There is a large number of such randomized response models in the literature S. L. Warner (e.g. [J. Am. Stat. Assoc. 60, No. 309, 63–69 (1965; Zbl 1298.62024)]). In this article, we propose and study a new indirect response model. We then derive a method of moments estimator for the unknown population mean of a stigmatizing variable, under the proposed model. We establish that if we decide to use noise added sensitive and innocuous responses then there is no need to do randomization on the responses, more specifically, it suffices to use just the noise added sensitive response. We then explore the possibility of obtaining an estimator based on maximization of likelihood or pseudolikelihood function. We then work in the Bayesian framework to explore the possibility of obtaining a Bayes or Bayeslike estimator based on the posterior distribution.
For the entire collection see [Zbl 1349.62001].

MSC:

62D05	Sampling theory, sample surveys
62F15	Bayesian inference

Keywords:

Bayeslike estimator; indirect response; randomized response; noise; Warner’s model; unrelated question model; Yu-Tian-Tang models; Kim-Warde model; Padmawar-Vijayan model; pure noise model; counting model; Poisson model; Bernoulli model