Stratified and two phase stratified estimation of sensitive character using conditional Quatember model

In this paper, we propose a conditional Quatember model that can efficiently estimate sensitive character by using the Quatember model only for those who answered “yes” through a random device composed of less sensitive character and forced answer questions. We derive estimates and variances for sensitive character and expressed the degree of privacy exposure risk using a hazard function. And in the conditional Quatember model, when the population proportion of unrelated character is unknown, it is developed into a conditional Quatember two-sample model that uses two independent samples when available. We suggest also a stratified conditional Quatember model when the population is composed of strata and deal with proportional and optimal method as a sample allocation method per each stratum and expand it to stratified conditional Quatember two-sample model which can be used when the population proportion of unrelated character is unknown. Finally, we compare the efficiencies between Quatember model and conditional Quatember one in view of variance and privacy protection, and compare stratified conditional Quatember model and stratified Quatember one and between stratified conditional Quatember model and stratified conditional Quatember two-sample model in view of variance.