Estimation of the finite population distribution function using a global penalized calibration method

J. A. Mayor-Gallego (), J. L. Moreno-Rebollo () and M. D. Jiménez-Gamero ()
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J. A. Mayor-Gallego: University of Seville
J. L. Moreno-Rebollo: University of Seville
M. D. Jiménez-Gamero: University of Seville

AStA Advances in Statistical Analysis, 2019, vol. 103, issue 1, No 1, 35 pages

Abstract: Abstract Auxiliary information $${\varvec{x}}$$ x is commonly used in survey sampling at the estimation stage. We propose an estimator of the finite population distribution function $$F_{y}(t)$$ F y ( t ) when $${\varvec{x}}$$ x is available for all units in the population and related to the study variable y by a superpopulation model. The new estimator integrates ideas from model calibration and penalized calibration. Calibration estimates of $$F_{y}(t)$$ F y ( t ) with the weights satisfying benchmark constraints on the fitted values distribution function $$\hat{F}_{\hat{y}}=F_{\hat{y}}$$ F ^ y ^ = F y ^ on a set of fixed values of t can be found in the literature. Alternatively, our proposal $$\hat{F}_{y\omega }$$ F ^ y ω seeks an estimator taking into account a global distance $$D(\hat{F}_{\hat{y}\omega },F_{\hat{y}})$$ D ( F ^ y ^ ω , F y ^ ) between $$\hat{F}_{\hat{y}\omega }$$ F ^ y ^ ω and $${F}_{\hat{y}},$$ F y ^ , and a penalty parameter $$\alpha $$ α that assesses the importance of this term in the objective function. The weights are explicitly obtained for the $$L^2$$ L 2 distance and conditions are given so that $$\hat{F}_{y\omega }$$ F ^ y ω to be a distribution function. In this case $$\hat{F}_{y\omega }$$ F ^ y ω can also be used to estimate the population quantiles. Moreover, results on the asymptotic unbiasedness and the asymptotic variance of $$\hat{F}_{y\omega }$$ F ^ y ω , for a fixed $$\alpha $$ α , are obtained. The results of a simulation study, designed to compare the proposed estimator to other existing ones, reveal that its performance is quite competitive.

Keywords: Auxiliary information; Model-assisted approach; Sample survey; Penalized calibration estimator (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10182-018-0321-z

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