Model based robust estimation of finite population total using the procedure of local linear regression

Abstract

Nonparametric regression provides an intensive estimation of unknown finite population parameters and is frequently used to explore the association between covariates and responses. This estimation procedure is more flexible and robust than inference based on design probabilities in design based inference or on parametric regression models in model based inference. In this study, model based robust estimators of finite population total are constructed using the procedure of local linear regression. In particular, robustness properties of the derived estimators are investigated and a brief comparison between the performances of the derived estimators and some existing estimators is made in terms of the biases, variances, mean square errors, relative efficiencies, confidence intervals and average lengths of confidence intervals. The study explores the use of adaptive bandwidth to handle sparse data. The local linear procedure is extended to stratified random sampling and to two stage cluster sampling. The local linear procedure is important in the sense that it adapts well to bias problems at boundaries and in regions of high curvature and it does not require smoothness and regularity conditions required by other methods such as the boundary kernels. It has been observed that the local linear regression estimators are generally asymptotically unbiased, efficient and consistent. The results for the biases show that the local linear regression estimators are superior and dominate the horvitz-thompson estimator and the linear regression estimator in all the relationships. The local linear regression estimators also dominate the dorfman estimator in all the relationships except when the relationship is quadratic. The results for the mean square errors indicate that the local linear regression estimators are more efficient and perform better than the horvitz-thompson and dorfman estimators, regardless of whether the underlying model is correctly specified or misspecified. The local linear regression estimators also outperform the linear regression estimator in all the relationships except when the relationship is linear. With respect to the relative efficiencies, results indicate that the local linear regression estimators are robust and are the most efficient estimators. The confidence intervals generated by the model based local linear method are much shorter than those generated by the design based horvitz-thompson method. The results also indicate that the model based approach performs better than the design based approach at 95% coverage rate. Generally, the model based approach outperforms the design based approach regardless of whether the underlying model is correctly specified or not but that effect decreases as the model variance increases.