On Studying the Relationship between the Ratio and the Regression Estimators for a Population Proportion
Juan F. Muñoz¹, Antonio Arcos², Encarnaciόn Άlvarez¹
¹Departament of Quantitative Methods in Economics and Business, University of Granada, Granada, Spain; ²Department of Statistics and O.R., University of Granada, Granada, Spain

Estimation of a proportion is commonly used in many areas and disciplines. Traditional estimators and confidence intervals (Blyth and Still, 1983; Cohen and Yang, 1994; Fleiss et al., 2003; Newcombe, 1998) for a population proportion does not assume auxiliary information at the estimation stage. Assuming auxiliary information, the ratio and regression methods are known techniques for the purpose of estimation of a population mean. They can be adapted to the problem of the estimation of the population proportion (see, for example Rueda et al., 2011a), although some differences can be observed. For example, a ratio estimator for a population proportion can be defined via a ratio estimator for the complementary of the population proportion. In this paper, we define an optimum ratio estimator for a population proportion and show that this estimator coincides with the regression estimator (Rueda et al. 2011b).

Blyth, C. R., Still, H. A. (1983). Binomial confidence intervals. J. Am. Stat. Assoc. 78: 108-116.

Cohen, G. R., Yang, S. Y. (1994). Mid-p confidence intervals for the Poisson expectation. Stat. Med. 13: 2189-2203.

Fleiss, J. L., Levin, B., Paik, M. C. (2003). Statistical methods for rates and proportions 3rd∼edn. Wiley, New Yersey.

Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Stat. Med. 17: 857-872.

Rueda, M.M., Muñoz, J.F., Arcos, A., Άlvarez, E. (2011a). Estimators and confidence intervals for the proportion using binary auxiliary information with applications to the estimation of prevalences. Biophamaceutical Statistics. In press.

Rueda, M.M., Muñoz, J.F., Arcos, A., Άlvarez, E. (2011b). Indirect estimation of proportions in natural resource surveys. Mathematics and Computers in Simulation. In press.

Keywords: Auxiliary information; Sample survey; Variance; inclusion probability

Biography: Juan F. Muñoz has some contributions to the literature of complex sample surveys. These include estimation of different parameters (means, totals, proportions, distribution functions, variances, quantiles), imputation, estimation via new procedures (pseudo empirical likelihood and calibration), etc.