A kernel method for estimating finite population distribution functions using auxiliary information

SUMMARY This paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population. A method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable. The resulting estimator compares favourably with existing estimators in terms of efficiency, conditional behaviour and robustness. The proposed method also has the advantage of producing estimates which are bona fide distribution functions. This is not the case for many calibration type estimators suggested in the literature. Finally, the proposed method is applicable under any probability sampling scheme.