Median Estimation in the Presence of Auxiliary Information

SUMMARY This paper deals with the estimation, under simple random sampling, of a finite population median in the presence of an auxiliary variable. An estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach. These estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known. On the basis of the asymptotic properties derived and some simulation results, the efficiencies of these estimators are compared. It is shown that the two estimators proposed, unlike that obtained from modifying the ratio estimator, always dominate the sample median in mean-squared error and that their efficiencies depend directly on the probability of ‘concordance’ rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable. When the linearity assumption is approximately satisfied, the three estimators are seen to have comparable efficiencies, while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumption.