Finite population distribution function estimation using P-Splines

Abstract

Estimating finite population distribution function (hereafter FPDF) is an important problem to the survey samplers since it summarizes almost all the relevant information of interest about the finite population. Chambers and Dunstan (1986) (henceforth CD) in their seminal paper propose a predictive estimator of FPDF incorporating the unit level auxiliary information available for the entire population. CD estimator assumes a linear regression model in the superpopulation. However, even for moderate deviation from linearity assumption, significant performance deterioration of CD estimator is observed. Here we propose a predictive estimator of FPDF based on a semiparametric regression model. For this we use recently developed penalized splines (P-splines) regression. The proposed estimator performs better than CD estimator if the linearity assumption fails. We find its asymptotic bias and variance. Finally, we compare the performance of the proposed estimator with other alternative estimators through simulation studies and illustrate its use with a real data set.