Comparison of some common ratio estimators using pitman measure of nearness

In this article we compare some common ratio estimators for estimating the population total of a given characteristic. The sampling schemes considered are simple random sampling (S.R.S.) and S.R.S. under stratification. The comparisons are made using the Pitman Nearness criterion under the model-based approach. The error term is assumed normal with mean zero and variance σ²(x). The function g(x) is a known function of the auxiliary variable x. Special interest is on the cases of g(x) =1 and x. The result is found the same as that using MSE criterion, although the PN is very different from the MSE intrinsically.