Finite mixtures model approach to sensitive questions in surveys

Shcherbina  Artem; Maiboroda  Rostyslav

doi:https://doi.org/10.59170/stattrans-2011-021

Finite mixtures model approach to sensitive questions in surveys

Shcherbina Artem National Taras Shevchenko University of Kyiv, Ukraine , Maiboroda Rostyslav National Taras Shevchenko University of Kyiv, Ukraine Statistics in Transition new series, vol. 12, 2011, 2, pages: 331-344 Published online: 3 October 2011 https://doi.org/10.59170/stattrans-2011-021

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ABSTRACT

Observations from mixtures of different subpopulations are common in biological and sociological studies. We consider the case, when the observations are taken from a set of groups containing subjects, which belong to different subpopulations. Proportion of each subpopulation in a group is known and can vary from group to group. Our aim is to estimate the means of an observed variable for subjects, which belong to each subpopulation. In this paper we consider the case, when subpopulations are defined by answers on so called “sensitive questions”. We consider some parametric and nonparametric estimates of the subpopulation means, such as weighted means, maximum likelihood and weighted least squares estimates. Finite sample properties of these estimates are analyzed. Mean square errors of the estimates are compared on simulated data. Some asymptotic results are also given

KEYWORDS

anonymous survey; sensitive questions; maximum likelihood; weighted mean; weighted least squares

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