On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys

Citation:
Pokhariya GP, Kikechi CB, Simwa RO. "On Local Linear Regression Estimation of Finite Population Totals in Model Based Surveys." American Journal of Theoretical and Applied Statistics. 2018;7((3)):92-101 .

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.
Keywords: Nonparametric Regression, Finite Population Totals, Local Linear Regression, Robustness Properties,
Confidence Intervals, Model Based Surveys

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