Combining Proportions From Several Randomized Response Models

by S.E. Ahmed and S. M. Khan .

Abstract: Randomized response (RR) techniques are helpful for obtaining data and protect respondent's privacy when studies are about sensitive characteristics. A large sample test for homogeneity of the proportions is developed. Simultaneous estimation of the proportions of RR models is developed in multi-sample situation. Preliminary test and Stein-type shrinkage estimators are proposed. The risk of the proposed estimators are derived and compared with each other. It is demonstrated that Stein-type estimators outperform the classical estimators. Moreover, it is shown that none of the preliminary test and shrinkage estimators dominate each other though they perform well relative to the classical estimators.

Key Words: Randomized response model, asymptotic distributional quadratic risk, local alternatives, preliminary test estimators and Stein-type shrinkage estimators

Authors:
S.E.Ahmed, ahmed@math.uregina.ca
S. M. Khan, khanso@meena.cc.uregina.ca

Editor: M. Ahsanullah , ahsan@genius.rider.edu

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