An extension of Franklin's randomized response technique for multi-proportions

ABSTRACT

In this article, we introduce six estimators, three based on row averages and the remaining three on column averages of population proportions for trichotomous population when randomized response sampling with a normal randomizing distribution is used. The estimators have been obtained using the method of moments. All the proposed estimators are shown to be unbiased and their variances have been worked out. The percent relative efficiencies of the column total based estimators with respect to row total based estimators are investigated through empirical study.

KEYWORDS:

• Estimator
• Randomized response technique
• Trichotomous population
• Unbiasedness and variance.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62D05

Acknowledgments

The authors are thankful to the Editor-in-Chief, Prof. N. Balakrishnan, the Editorial Assistant Ms. Dobbie Iscoe and a referee, an expert in randomized response techniques, for their help in bringing the original manuscript to its present form.