In survey sampling statisticians often make estimation of population parameters. This can be done using a number of the available approaches which include design-based, model-based, model-assisted or randomization-assisted model based approach. In this paper regression estimation under model based approach has been studied. In regression estimation, researchers can opt to use parametric or nonparametric estimation technique. Because of the challenges that one can encounter as a result of model misspecification in the parametric type of regression, the nonparametric regression has become popular especially in the recent past. This paper explores this type of regression estimation. Kernel estimation usually forms an integral part in this type of regression. There are a number of functions available for such a use. The goal of this study is to compare the performance of the different nonparametric regression estimators (the finite population total estimator due Dorfman (1992), the proposed finite population total estimator that incorporates reflection technique in modifying the kernel smoother), the ratio estimator and the design-based Horvitz-Thompson estimator. To achieve this, data was simulated using a number of commonly used models. From this data the assessment of the estimators mentioned above has been done using the conditional biases. Confidence intervals have also been constructed with a view to determining the better estimator of those studied. The findings indicate that proposed estimator of finite population total that is nonparametric and uses data reflection technique is better in the context of the analysis done.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 9, Issue 4) |
| DOI | 10.11648/j.ajtas.20200904.13 |
| Page(s) | 101-105 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2020. Published by Science Publishing Group |
Conditional Biases, Reflection Technique, Confidence Lengths, Nonparametric Regression Estimation
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APA Style
Langat Reuben Cheruiyot. (2020). Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study. American Journal of Theoretical and Applied Statistics, 9(4), 101-105. https://doi.org/10.11648/j.ajtas.20200904.13
ACS Style
Langat Reuben Cheruiyot. Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study. Am. J. Theor. Appl. Stat. 2020, 9(4), 101-105. doi: 10.11648/j.ajtas.20200904.13
AMA Style
Langat Reuben Cheruiyot. Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study. Am J Theor Appl Stat. 2020;9(4):101-105. doi: 10.11648/j.ajtas.20200904.13
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Download@article{10.11648/j.ajtas.20200904.13,
author = {Langat Reuben Cheruiyot},
title = {Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {9},
number = {4},
pages = {101-105},
doi = {10.11648/j.ajtas.20200904.13},
url = {https://doi.org/10.11648/j.ajtas.20200904.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200904.13},
abstract = {In survey sampling statisticians often make estimation of population parameters. This can be done using a number of the available approaches which include design-based, model-based, model-assisted or randomization-assisted model based approach. In this paper regression estimation under model based approach has been studied. In regression estimation, researchers can opt to use parametric or nonparametric estimation technique. Because of the challenges that one can encounter as a result of model misspecification in the parametric type of regression, the nonparametric regression has become popular especially in the recent past. This paper explores this type of regression estimation. Kernel estimation usually forms an integral part in this type of regression. There are a number of functions available for such a use. The goal of this study is to compare the performance of the different nonparametric regression estimators (the finite population total estimator due Dorfman (1992), the proposed finite population total estimator that incorporates reflection technique in modifying the kernel smoother), the ratio estimator and the design-based Horvitz-Thompson estimator. To achieve this, data was simulated using a number of commonly used models. From this data the assessment of the estimators mentioned above has been done using the conditional biases. Confidence intervals have also been constructed with a view to determining the better estimator of those studied. The findings indicate that proposed estimator of finite population total that is nonparametric and uses data reflection technique is better in the context of the analysis done.},
year = {2020}
}
TY - JOUR T1 - Exploring Data-Reflection Technique in Nonparametric Regression Estimation of Finite Population Total: An Empirical Study AU - Langat Reuben Cheruiyot Y1 - 2020/06/03 PY - 2020 N1 - https://doi.org/10.11648/j.ajtas.20200904.13 DO - 10.11648/j.ajtas.20200904.13 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 101 EP - 105 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20200904.13 AB - In survey sampling statisticians often make estimation of population parameters. This can be done using a number of the available approaches which include design-based, model-based, model-assisted or randomization-assisted model based approach. In this paper regression estimation under model based approach has been studied. In regression estimation, researchers can opt to use parametric or nonparametric estimation technique. Because of the challenges that one can encounter as a result of model misspecification in the parametric type of regression, the nonparametric regression has become popular especially in the recent past. This paper explores this type of regression estimation. Kernel estimation usually forms an integral part in this type of regression. There are a number of functions available for such a use. The goal of this study is to compare the performance of the different nonparametric regression estimators (the finite population total estimator due Dorfman (1992), the proposed finite population total estimator that incorporates reflection technique in modifying the kernel smoother), the ratio estimator and the design-based Horvitz-Thompson estimator. To achieve this, data was simulated using a number of commonly used models. From this data the assessment of the estimators mentioned above has been done using the conditional biases. Confidence intervals have also been constructed with a view to determining the better estimator of those studied. The findings indicate that proposed estimator of finite population total that is nonparametric and uses data reflection technique is better in the context of the analysis done. VL - 9 IS - 4 ER -
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