Abstract
In survey sampling, the main objective is to make inference about the entire population parameters using the sample statistics. In this study, a nonparametric estimator of finite population total is proposed and the coverage probabilities using the Edgeworth expansion explored. Three properties; unbiasedness, efficiency and the confidence interval of the proposed estimator are studied. There is a lot of literature on study of two properties; unbiasedness and efficiency of the finite population total. This study therefore has more focus on confidence interval and coverage probability. The amount of bias and MSE are studied partially analytically, followed by an empirical study on the two properties and the confidence interval of the proposed estimator. Based on the empirical study with simulations in R, the proposed estimator resulted into smaller bias and MSE compared to the nonparametric estimator due to [6], the design-based Horvitz-Thompson estimator and the model-based ratio estimator. Further, the proposed estimator is tighter compared to the other three considered in this study and has higher converging coverage probabilities.
Highlights
In estimating a population parameter such as a mean or a variance, a measure of precision of the estimate is quite paramount
Jacob Oketch Okungu et al.: Non-parametric Estimator for a Finite Population Total Based on Edgeworth Expansion population
To propose a nonparametric estimator for a finite population total based on Edgeworth expansion
Summary
In estimating a population parameter such as a mean or a variance, a measure of precision of the estimate is quite paramount. Efforts have been made to explore alternative ways to attenuate the errors These include the use of nonparametric regression in evolving robust estimators in finite population sampling [11]. The non-parametric regression estimator of a finite population total is a potent rival to familiar design-based estimators. It has the quality of automaticity associated with design-based estimators, but can better reflect the actual structure of the data, yielding greater efficiency [7]. It can be costly in computer power, and will probably not do as well as a parametric-model based estimator, when the modelling process is done carefully. Further research on how satisfactory the consequent confidence intervals of the estimator could be [6]
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