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

Mayor-Gallego, J. A.; Moreno-Rebollo, J. L.; Jiménez Gamero, María Dolores

Abstract:

Auxiliary information x is commonly used in survey sampling at the estimation stage. We propose an estimator of the finite population distribution function Fy(t) when 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 Fy(t) with the weights satisfying benchmark constraints on the fitted values distribution function ˆFˆy = Fˆy on a set of fixed values of t can be found in the literature. Alternatively, our proposal ˆF yω seeks an estimator taking into account a global distance D( ˆF ˆyω, Fˆy) between ˆF ˆyω and Fˆy , and a penalty parameter α that assesses the importance of this term in the objective function. The weights are explicitly obtained for the L2 distance and conditions are given so that ˆFyω to be a distribution function. In this case ˆFyω can also be used to estimate the population quantiles. Moreover, results on the asymptotic unbiasedness and the asymptotic variance of ˆFyω, for a fixed 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.

Year:

2019

Type of Publication:

Article

Keywords:

Auxiliary information; Model assisted approach; Sample survey; Penalized calibration estimator

Journal:

AStA Advances in Statistical Analysis

Volume:

103

Number:

1

Pages:

1-35

Month:

March

Note:

Q4 99/123 h-index 0,643 (JCR2018)

Comments:

MTM2014-55966-P and MTM2017-89422-P

DOI:

10.1007/s10182-018-0321-z