Browsing by Author "Pokhariyal, Ganesh Prasad"

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    On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys
    (American Journal of Theoretical and Applied Statistics, 2018) Kikechi, Conlet Biketi; Simwa, Richard Onyino; Pokhariyal, Ganesh Prasad
    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.
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    On Prediction Based Robust Estimators of Finite Population Totals
    (International Journal of Statistics and Applied Mathematics, 2019) Kikechi, Conlet Biketi; Simwa, Richard Onyino; Pokhariyal, Ganesh Prasad
    In this article, we present results on nonparametric regression for estimating unknown finite population totals in a model based framework. Consistent robust estimators of finite population totals are derived using the procedure of local polynomial regression and their robustness properties studied (See Kikechi et al. (2017), Kikechi et al. (2018) and Kikechi and Simwa (2018)). Results of the bias show that the Local Polynomial estimators dominate the Horvitz-Thompson estimator for the linear, quadratic, bump and jump populations. Further, the biases under the model based Local Polynomial approach are much lower than those under the design based Horvitz-Thompson approach in different populations. The MSE results show that the Local Linear Regression estimators are performing better than the HorvitzThompson and Dorfman estimators, irrespective of the model specification or misspecification. Results further indicate that the confidence intervals generated by the model based Local Polynomial procedure are much tighter than those generated by the design based Horvitz-Thompson method, regardless of whether the model is specified or misspecified. It has been observed that the model based approach outperforms the design based approach at 95% coverage rate. In terms of their efficiency, and in comparison with other estimators that exist in the literature, it is observed that the Local Polynomial Regression estimators are robust and are the most efficient estimators. Generally, the Local Polynomial Regression estimators are not only superior to the popular Kernel Regression estimators, but they are also the best among all linear smoothers including those produced by orthogonal series and spline methods. The estimators adapt well to bias problems at boundaries and in regions of high curvature and they do not require smoothness and regularity conditions required by other methods such as the boundary Kernels.