Samuel Joel Kamun*

Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Kenya Nairobi, Mombasa, Kenya

*Corresponding Author: Samuel Joel Kamun, Department of Mathematics and Actuarial Sciences, Catholic University of Eastern Africa, Kenya Nairobi, Mombasa, Kenya.

Received: December 16, 2022; Published: January 09, 2023

Abstract

The analysis of sample-based studies involving sampling designs for small sample sizes is challenging because the sample selection probabilities (as well as the sample weights) are dependent on the response variable and covariates. This research focused on nonparametric weighted linear models in order to find more precise estimators with lower sample bias. The study has used rank-based approaches because they outperform least-squares procedures when the data deviates from normality and/or contains outliers. Weights can be added to these approaches to create weighted strategies (WT). In this paper, we demonstrate how to construct WT estimates using rank-based regression. Rank-based estimators were developed to provide a nonparametric, robust alternative to traditional likelihood or least squares estimators. They are then used to generate estimates with higher relative efficiencies and lower finite small sample bias than the Horvitz-Thompson weighted estimator with unmodified weight. The purpose of our study is to compare estimators using the reciprocal of the sample inclusion probabilities and other weights derived by modifying and rescaling them using relative efficiency, sample bias, and standard error for small sample sizes. The constructed estimates using different modified and rescaled weights are actually the weighted nonparametric estimators. The study compared three new estimators for both the unmodified and modified weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from the conventional Horvitz-Thompson weighted estimator.

Keywords: Small Samples; Estimators; Relative Efficiency; Sample Bias; Standard Error

References

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5. Kamun SJ., et al. “On Derivation of the Semi-Parametric Weighted Likelihood Estimator, SPW, and the Weighted Conditional Pseudo Likelihood Estimator, WCPE”. Far East Journal of Theoretical Statistics © 2021 Pushpa Publishing House, Prayagraj, 62.2 (2021): 81-90.
6. Kamun S J., et al. “Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE”. American Journal of Theoretical and Applied Statistics4 (2021): 202-207.
7. Kamun SJ. “On Derivation of Non-Parametric Weighted Linear Models”. IJIRSE 12 (2022): 25-30.
8. 04 (2018): 562-569+576.

Citation

Citation: Samuel Joel Kamun. “A Comparison of Non-Parametric Weighted Linear Models". Acta Scientific Computer Sciences 5.2 (2023): 03-09.

Copyright

Copyright: © 2023 Samuel Joel Kamun. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.