Non-parametric regression estimation of a finite Population total in the presence of Heteroscedasticity

Abstract

Non parametric regression provides computationally intensive estimation.of unknown finite population quantities. Such estimation is usually more flexible and robust than inferences tied to design - probabilities (in design-based inference) or to parametric regression models in (model-based inference). Dorfman [9] used a more general super population model to find a non-parametric regression based estimator for the population total T . He, however, assumed homoscedasticity when constructing his proposed estimator. In his empirical study, he noted that the data showed clear signs of heteroscedasticity. In this study we consider the improvement in the efficiency of Dorfman's non-parametric regression based estimator of a finite population. To do this we incorporate a reasonable assumption of variance structure into the non-parametric regression methodology and use the weighted least squares method to obtain the proposed non-parametric regression based estimator. In our empirical work we have used two kinds of data sets: simulated and secondary data. The simulated data is of two kinds: homoscedastic and heteroscedastic generated with the help of Genstat 8th edition statistical application package. The secondary data was obtained from the internet from the United States Bureau of Labor Statistics. By calculating Dorfman's and our population estimates based on the given data sets using Dorfman's and our proposed estimator's respectively, we have established that our proposed estimator is more efficient than Dorfman's, that is, the efficiency of Dorfman's non-parametric regression based estimator has been improved when we put into account heteroscedasticity.