Comparison of Ratio Estimators with Two Auxiliary Variables

Many estimators of the population parameters are constructed using known auxiliary variables. The classical well known ratio estimator is one of them. Ratio estimators are frequently employed in sample surveys when estimating the population mean Y of a variate Y with the help of the known population means of a correlated auxiliary variables. Various improvements of this ratio estimator have been considered by many authors. Some estimators use two auxiliary variables. Some other use groups of estimators are composite. In case two auxiliary variables are known, the ratio-cum-product estimator may be used. It is well known that when the auxiliary information is to be used at the estimation stage, the ratio, product and regression estimators are widely utilized in many situations. There are no analytical procedures to compare the ratio estimators, since their mean square errors are approximated up to some extent. Theoretically, it is hard to compare the bias, mean square error, skewness and kurtosis of the estimators over the other estimators. However, we can compute these of the estimators using Monte Carlo simulation. This method is suitable when the theoretical comparisons fail. In this paper, some ratio estimators with two auxiliary variables available in literature are reviewed and their efficiencies are compared by simulation for different distributions with known correlation coefficients. The results show that the simulation method is more appropriate when there is no closed expression for the bias and mean squared error of the estimators.