Variance estimation for non-parametric regression model in systematic sampling under heteroscedastic errors: a simulation study

Systematic sampling is an attractive tool for surveys as it is easily implemented and has an efficient design. In a systematic sample, an important problem is the unavailability of any direct estimator of design variance. A non-parametric model is flexible as it can be applied in different situations with auxiliary variables considered at the population level. Here, different estimators for a non-parametric model are considered for a given population using LPR as an estimation technique for multiple levels of heteroscedastic errors. For comparison, a simulation study is performed for different estimators. This comparison measures the relative bias and mean squared error. It is evident that the local polynomial non-parametric estimator performs well in our proposed situation.