Abstract
In this study a model based approach is adopted and a robust estimator of the jackknifed Nadaraya Watson estimator of the finite population total is proposed by incorporating the jackknifed procedure into the nonparametric regression estimator (the case of Nadaraya Watson). The study sought to estimate the finite population total using the proposed estimator (Jackknifed Nadaraya Watson). The study also looked at the various approaches of estimation of finite population totals and their properties. To measure the performance of each estimator, the study considered the average bias, the efficiency by the use of mean squared error and robustness using the rate of change of efficiency. Numerical study using simulated population was employed to examine the performance of the proposed estimator and compared it with the already existing estimators (Horvitz-Thompson, Nadaraya Watson, Ratio estimator). The simulation experiment showed that the proposed estimator records better results in terms of Bias and mean squared errors (MSE).
Highlights
In many complex surveys, available information about the study population can be used at the design and estimation stages to construct efficient procedures for the finite population quantities i.e. population total or mean so as to increase the precision of the estimators of such population quantities
Total Using Nadaraya Watson Incorporating Jackknifing case where jackknifing procedure is incorporated into the Nadaraya Watson estimator
Dorfman [3] introduced a non-parametric regression estimator for finite population total based on a sample drawn from the population
Summary
Available information about the study population can be used at the design and estimation stages to construct efficient procedures for the finite population quantities i.e. population total or mean so as to increase the precision of the estimators of such population quantities. For efficient use of any of these estimators prior knowledge of the specific parametric structure of the population needs to be known and this is usually problematic especially if the model is to be used for many variables [1] Because of these concerns more focus has been given to non-parametric models describing the relationship between the auxiliary variables and the study variables are assumed [2]. [7] Improved on [6] estimator and developed a model-based local polynomial regression estimator applicable to direct sampling designs i.e. simple random sampling and systematic sampling. In this study auxiliary information is used to determine the estimate of finite population total using non-parametric regression in the Imboga Orang’o Herbert et al.: Optimal Nonparametric Regression Estimation of Finite Population. Total Using Nadaraya Watson Incorporating Jackknifing case where jackknifing procedure is incorporated into the Nadaraya Watson estimator
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