A Modified Nadaraya-Watson Estimator for the Variance of the Finite Population Mean

Charlotte K Mokaya^1, and DR. Edward Gachangi Njenga¹

¹Department of Mathematics, Kenyatta University, Nairobi, Kenya

Cite this paper

Charlotte K Mokaya and DR. Edward Gachangi Njenga. A Modified Nadaraya-Watson Estimator for the Variance of the Finite Population Mean. American Journal of Applied Mathematics and Statistics. 2019; 7(4):146-151. doi: 10.12691/AJAMS-7-4-4

Abstract

The main objective of this study was to derive a nonparametric estimator for the variance of the population mean when the population structure is nonlinear and heteroscedastic. Therefore, this paper sought to investigate the performance of Nadaraya-Watson estimator with a variable bandwidth. The methodology was derived by modifying the Nadaraya-Watson estimator where the bandwidth was a function of the range of observations. The performance of the proposed estimator was compared with other estimators i.e. Ratio estimator and Nadaraya-Watson with a fixed bandwidth. To measure performance of each of the estimators, average mean squared error was considered. It was found out that the Ratio estimator performs well for linear and homoscedastic populations while the Nadaraya-Watson with fixed bandwidth performs well for nonlinear and heteroscedastic populations. However, in the light of these findings, Nadaraya-Watson estimator (with variable bandwidth) was found to perform better and most efficient than the Ratio estimator and Nadaraya-Watson estimator (with fixed bandwidth) in nonlinear and heteroscedastic populations. It was also found to be the most robust compared to the estimators considered in this study.

Keywords

bandwidth, Nadaraya-Watson, robust, efficiency

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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