An Improved Product Estimator for Finite Population Mean in the Presence of Nonignorable Nonresponse

The existence of non-linear relationship between study and auxiliary variable may show a false positive or negative correlation between them. This challenge coupled with nonresponse will lead to bias estimate and wrong conclusions. Therefore, this study developed an improved estimator for finite population mean when nonignorable nonresponse is present. With the aid of auxiliary variable, using stratified random sampling, the study proposed an estimator using the direct generalized ratio estimator. Statistical properties of the proposed estimator such as bias and mean square error up to second order of approximation were obtained. Simulation and empirical studies were performed on the derived statistical properties of the proposed estimator using linear and nonlinear populations. The simulation and empirical studies indicated that the proposed estimator (ℝDG,2,i) works better with nonlinear population. The numerical demonstrations further indicated that proposed estimator was found to be less bias and more consistent but less ecient in terms of mean square error when compared with that of Ashutosh [1]. Therefore, the referenced estimator may prove to be useful when the focus is on inference. However, when emphasis shifts to estimation, the proposed estimator (ℝDG,2,i) is preferred.