International Journal of Theoretical and Applied Mathematics 2017; 3(3): 122-128 http://www.sciencepublishinggroup.com/j/ijtam doi: 10.11648/j.ijtam.20170303.14 Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya Email address: imbogaherbert@yahoo.com (I. O. Herbert) To cite this article: Imboga Orang’o Herbert, George Otieno Orwa, Romanus Odhiambo Otieno. Optimal Nonparametric Regression Estimation of Finite Population Total Using Nadaraya Watson Incorporating Jackknifing. International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 3, 2017, pp. 122-128. doi: 10.11648/j.ijtam.20170303.14 Received: April 17, 2017; Accepted: May 27, 2017; Published: June 30, 2017 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). Keywords: Homoscedasticity, Jackknifing, Optimal, Robustness, Efficiency 1. Introduction 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. The information can be collected by national census, official registers, natural resources inventories and remote sensing data. Estimation being the main concern in surveys, emphasis is usually on the use of the auxiliary information. One of the approaches is to assume a working model and more often a linear model describing the relationship between the survey variable and auxiliary variable is selected. Estimators are then derived from this linear model. However 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]. The idea of nonparametric traces its origin in works by [3]. Non-parametric based estimation is often more robust and flexible than inference based on parametric regression models or design probabilities (as in the case of design-based inference) [4]. A variety of approaches exist in the construction of more efficient estimators and they include; Model-based and design based methods. In Model- based approach, the idea is based on super population models which assumes that the population under study is a realization of a random variable having a super population model . The model  is used to predict the non-sampled values of the population hence finite population quantities [5]. [6] First considered non parametric models for  and obtained a local polynomial regression estimator as a generalization of the ordinary generalized regression estimator. From the simulation, their study showed the proposed estimator performed better than the other parametric estimators. [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. Their estimator demonstrated better results than [7]. In this study auxiliary information is used to determine the estimate of finite population total using non-parametric regression in the