Optimum design-based ratio estimators of the distribution function |
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| Authors: | JF Muñoz E Álvarez M Rueda |
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| Institution: | 1. Department of Quantitative Methods in Economics and Business, University of Granada, 18071 Granada, Spain;2. Centro Universitario de la Defensa, Polytechnic University of Cartagena, 30720 San Javier, Murcia, Spain;3. Department of Statistics and O.R. University of Granada, 18071 Granada, Spain |
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| Abstract: | The ratio method is commonly used to the estimation of means and totals. This method was extended to the problem of estimating the distribution function. An alternative ratio estimator of the distribution function is defined. A result that compares the variances of the aforementioned ratio estimators is used to define optimum design-based ratio estimators of the distribution function. Different empirical results indicate that the optimum ratio estimators can be more efficient than alternative ratio estimators. In addition, we show by simulations that alternative ratio estimators can have large biases, whereas biases of the optimum ratio estimators are negligible in this situation. |
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| Keywords: | auxiliary information variance quantile low income proportion inclusion probability |
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