Challenges with Dual Use of Auxiliary Variable: A Class of Estimators for Population Mean

The estimation of finite population mean is always of interest for different sampling techniques and it is the basic measure to find for sample to estimate one of the most applicable central tendency. In literature, under simple random sampling without replacement people used rank or empirical distribution function as dual use of an auxiliary variable in estimation method to improve the efficiency of the estimator. In this paper, we proposed a class of regression-cum-exponential estimator using two auxiliary variables and also the dual use of one of the auxiliary variables in the form of its empirical distribution function. The mean square error of the proposed estimator in derived and compared with existing estimators using empirical study based on real life populations. The simulation study is also conducted to assess the sampling stability using empirical mean square error. The results show that the proposed estimator is performing much better than its competitors not due the dual use of auxiliary variables rather using additional suitable auxiliary variable. The study concludes that dual use of auxiliary variable is not the right choice to improve the efficiency of an estimator rather using additional auxiliary variable(s).