Linear Models for Randomized Response Designs

Abstract

Linear models, based on random permutation models, are developed to include a wide class of one-sample randomized response designs. The general form of the “optimal” estimator of the finite population mean or proportion is obtained. Most of the conventional randomized response estimators are seen to be optimal, in terms of minimum average mean squared error, within their associated designs. The optimality results are obtained for sampling without replacement and include extensions of randomized response designs to unequal probability sampling.

Key Words:

• Minimum mean squared error estimation
• Random permutation models
• Randomized response
• Response errors
• Unequal probability sampling