Assessing the adequacy of first order approximations in ratio type estimators

In many papers the first order approximation of the theoretical mean square error has been used for the ratio type estimators for the population mean and variance. The main focus of this paper is on examining the adequacy of the first order approximation and also on examining the robustness of estimators. We have calculated the theoretical mean square errors for many ratio type estimators, based on the first order approximation, and the corresponding empirical mean square errors. We observe that the first order approximation for ratio type mean estimators works well if the sampling fraction is small. We also observe that departure from the assumption of bivariate normality is not a serious handicap for large samples.