Optimum ratio estimators for the population proportion

Abstract

The problem of the estimation of a population proportion using auxiliary information has been recently studied by Rueda et al. (Estimators and confidence intervals for the proportion using binary auxiliary information with applications to pharmaceutical studies, J. Biopharmaceut. Statist. 21 (2011), pp. 526–554), which proposed several ratio estimators of the population proportion and studied some theoretical properties. In this paper, we define a new ratio estimator based on a linear combination of two ratio estimators defined by Rueda et al. (2011). The variance of the new estimator is calculated and it is used to obtain the optimum value into the linear combination in the sense of minimal variance. Theoretical and empirical studies show that the suggested ratio estimator performs better than alternative estimators.

Keywords:

• auxiliary information
• ratio-type estimator
• proportion estimation
• finite population
• simple random sampling

2000 AMS Subject Classification :

• 62D05

Acknowledgements

The authors would like to thank the referees for their many helpful comments and suggestions. This work is partially supported by Ministerio de Educación y Ciencia (contract No. MTM2009-10055).