Abstract
In this paper, nonparametric regression is employed which provides an estimation of unknown finite population totals. A robust estimator of finite population totals in model based inference is constructed using the procedure of local linear regression. In particular, robustness properties of the proposed estimator are derived and a brief comparison between the performances of the derived estimator and some existing estimators is made in terms of bias, MSE and relative efficiency. Results indicate that the local linear regression estimator is more efficient and performing better than the Horvitz-Thompson and Dorfman estimators, regardless of whether the model is specified or mispecified. The local linear regression estimator also outperforms the linear regression estimator in all the populations except when the population is linear. The confidence intervals generated by the model based local linear regression method are much tighter than those generated by the design based Horvitz-Thompson method. 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.
Highlights
Integrated systems for survey designs and estimation methods to finite population inference have been considered by researchers in the past and categorised as design based approach, model assisted approach, combined inference approach and model based approach
The following assumptions made in Ruppert and Wand [16] are used to derive the properties of the local linear regression estimator: (i) The variables lie in the interval 0, 1 . (ii) The function, . is bounded and continuous on 0, 1 . (iii) The kernel & 2 is symmetric and supported on −1, 1
The confidence intervals generated by the model based Local Linear method are much tighter than those generated by the design based Horvitz-Thompson method, regardless of whether the model is specified or mispecified
Summary
Integrated systems for survey designs and estimation methods to finite population inference have been considered by researchers in the past and categorised as design based approach, model assisted approach, combined inference approach and model based approach. A new type of model-assisted non-parametric regression estimator for the finite population total, based on local polynomial smoothing which is a generalization of kernel regression has been proposed. Breidt and Opsomer [13] use the traditional local polynomial regression estimator for the unknown regression function for the model assisted estimation of the finite population total. Simulation studies showed that the bias of the modified nonparametric regression estimator had the same leading terms and order of probability as under the model based framework. He develops asymptotic properties under the combined inference approach and tests the performance of the estimator against the traditional model based local constant estimators. The use of local linear regression procedure in a purely model based framework is open and requires further study
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