Extensions of Some Randomized Response Procedures Related with Gupta-Thornton Method: The Use of Order Statistics

Abstract

Abstract We consider the problem of estimating the mean of a sensitive quantitative variable Y. The seminal work of Warner (1965) on randomized response has motivated the development of a fruitful theory. Gupta-Thornton (2002) proposed a method for scrambling the sensitive variable using an auxiliary variable X of known distribution. We propose using this distribution for generating order statistics. This chapter is concerned with the development of alternative scrambling procedures, which use order statistics of X. A comparison is developed in terms of the variance of the involved estimators.