Horvitz-Thompson estimation with randomized response and nonresponse

Issue title: Randomized Response Techniques

Guest editors: Sarjinder Singh

Article type: Research Article

Authors: Barabesi, Lucio^a | Diana, Giancarlo^b | Perri, Pier Francesco^{c; *}

Affiliations: [a] Department of Economics and Statistics, University of Siena, Siena, Italy | [b] Department of Statistical Sciences, University of Padova, Padova, Italy | [c] Department of Economics, Statistics and Finance, University of Calabria, Arcavacata di Rende, Italy

Correspondence: [*] Corresponding author: Pier Francesco Perri, Department of Economics, Statistics and Finance, University of Calabria, Via P. Bucci, 87036 Arcavacata di Rende, Italy. E-mail: [email protected].

Abstract: We consider the nonstandard situation where the randomized response theory is applied in a nonresponse set-up. The customary Horvitz-Thompson estimator for the population total of a sensitive variable is adjusted to take into account missing data, true response and randomized response, and the expression of its variance and the corresponding estimator provided. Finally, a numerical study is carried out to investigate how the estimation process can be affected by scrambled responses and how possible improvements in respondent cooperation can compensate for certain levels of nonresponse.

Keywords: Horvitz-Thompson estimator, multiplicative model, relative efficiency loss, variance estimator

DOI: 10.3233/MAS-130274

Journal: Model Assisted Statistics and Applications, vol. 9, no. 1, pp. 3-10, 2014