Calibration Approach Ratio Estimators of Population Median in Stratified Random Sampling Design
C. S. Agbebia *
Department of Statistics, University of Cross River State, Calabar, Nigeria.
E. I. Enang
Department of Statistics, University of Calabar, Calabar, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Median as a measure of location gives a more robust estimate than the mean when dealing with heavy tailed or skewed distributions. It can also be used in cases of qualitative variables and open end intervals. Calibration, an approach that adjusts the original design weight by incorporating auxiliary information is employed using the chi square distance measure on a ratio median estimator under stratified random sampling to propose some estimators of population median. These proposed estimators are: the regression and ratio-type calibrated estimators with one constraint and the regression and ratio-type calibrated estimators with two constraints. The estimators of variance of these proposed estimators are also obtained. Empirical investigations on the performance of these estimators are carried out using R software simulated data set under underlying distributional assumptions of Cauchy and Lognormal, for sample sizes of 10%, 20% and 25%. The results showed that the proposed regression and ratio-type calibrated estimators with one constraint and the regression-type calibrated estimator with two constraints were more efficient than the existing ratio estimator and the proposed ratio-type calibrated estimator under two constraints for both Cauchy and the lognormal distributions.
Keywords: Median, calibration, ratio-type estimator, regression-type estimator, stratified random sampling, auxiliary variables etc