Kernel density estimation using additive randomized response technique (RRT) models

Abstract

In 2002 Ahmad (Ahmad 2002) introduced the kernel density estimation of the density curve of a sensitive variable based on multiplicative RRT models and provided some theoretical results. In this article, we propose a kernel density estimator in the context of additive RRT models, which are more commonly used in the field of survey sampling. A simulation study is presented to validate the theoretical results from the previous work of Ahmad (Ahmad 2002), and also compare the performances of the kernel density estimators based on the additive and multiplicative RRT models. Simulations show that the proposed kernel density estimator using additive scrambling performs better than the one using multiplicative scrambling, and it allows more error in the bandwidth selection in kernel density estimation.