Estimation of Population Median under Robust Measures of an Auxiliary Variable

Abstract

In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

Efficient class of ratio cum median estimators for estimating the population median

“…On the other hand, it is also observed that the [8,9] estimators are more efficient than our proposed class of estimators, even at optimality conditions. This is indicated as the Mean squared errors of these estimators are less than the proposed class of estimators in the four populations.…”

“…From the works of [ 9 ] their proposed estimators are more efficient than [ 8 ] estimator. Therefore, [ 9 ] estimators are more efficient than proposed estimator.…”

“…Remarks: As it is stated that the estimators of [ 8 , 9 ] are more efficient than the proposed estimator, however the practical applications of these estimators in the field become a bit cumbersome and sometimes almost infeasible because of the presence of the unknown parameters in the estimators. Even if the estimators of these unknown parameters could be determined, they may turn out to be biased.…”

“…The increase in efficiency of these estimators is due to the presence of many unknown parameter estimates, since it is a well-known fact that MSE is a function of the number of parameters present. Hence, the proposed class of median estimators outcompete [ 8 , 9 ] estimators, in terms of their simplicity convenience in application.…”

“…For more works on estimators of population median, we refer the readers to [7][8][9]. [10] Considered the randomized response method in estimating the population ratio based on ranked set sampling.…”