Improved estimator for estimation of population mean using predictive approach under PPS sampling

In this study, we apply a predictive approach to the problem of finding new estimators for the estimation of finite population mean using auxiliary variable under probability proportional to size (PPS) sampling. This work is deemed novel due to the fact that, as far as we are aware, no one has before investigated the predictive approach to estimating the finite population mean under probability proportional to size sampling. The expressions for the bias and mean square error (MSE) are derived up to the first order. In order to verify the theoretical results, numerical and simulation investigations are conducted respectively. Based on the numerical result, it is shown that the suggested estimator performs well in terms of minimum MSE and higher percentage relative efficiency (PRE). The conditions under which the suggested estimator is more efficient than the other estimators are described numerically.