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Title: Estimation of the finite population distribution function using a global penalized calibration method Authors:  Maria Dolores Jimenez-Gamero - Universidad de Sevilla (Spain) [presenting]
Jose Antonio Mayor-Gallego - University of Sevilla (Spain)
Juan Luis Moreno-Rebollo - Seville (Spain)
Abstract: An estimator of the finite population distribution function $F_{y}(t)$ when auxiliary variables ${x}$, related to the study variable $y$ by a superpopulation model, are available, is proposed. The new estimator integrates ideas from model calibration, and penalized calibration. Alternatively to other model based calibration estimates of $F_{y}(t)$ in the literature, which require the distribution function estimation of the fitted values to be equal to the distribution function of the fitted values on some fixed points, a penalty term that measures the distance between the distribution function of the fitted values and its estimate, is included in the objective function. Thus, in a sense, it is imposed on both distribution functions be close at all points. Conditions are given so that the proposed estimate to be a proper distribution function. Results on the asymptotic unbiasedness and the asymptotic variance of the proposed estimator are obtained. In a simulation study the proposed estimator has better performance than others in the literature.