The precision of an estimator is at times discussed regarding the variance. Usually, the exact value of the variance is unknown. The discussion relies on unknown populace quantities. When a researcher obtains the survey data, an estimate of the variance can, therefore, be calculated. When survey results are presented, it is good practice to provide variance estimates for the estimator used in the study. The estimator of the variance can further be used to construct confidence interval, assuming that the sampling distribution of estimator is approximately normal. This study proposes estimation of standard error and confidence interval for a nonparametric regression estimator for a finite population using bootstrapping method. The idea behind bootstrapping is to carry out computations on the collected data. Computation activity assists in estimating the disparity of statistics that are themselves computed from the same data. The variance of the Nadaraya-Watson estimator is derived, based on bootstrap procedure. This operation has led to the derivation of confidence interval associated with Nadaraya-Watson estimator of the population total. A simulation study has been carried out. The overall conclusion is that the confidence interval associated with Nadaraya-Watson estimator is tighter than all the other estimators (Horvitz-Thompson estimator, Local linear estimator, and Ratio estimator).
| Published in | American Journal of Theoretical and Applied Statistics (Volume 6, Issue 2) |
| DOI | 10.11648/j.ajtas.20170602.17 |
| Page(s) | 117-122 |
| 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. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Bootstrap, Nonparametric Regression Model, Confidence Interval, Finite Population Total
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APA Style
Nicholas Makumi, Romanus Odhiambo, George Otieno Orwa, Stellamaris Adhiambo. (2017). On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total. American Journal of Theoretical and Applied Statistics, 6(2), 117-122. https://doi.org/10.11648/j.ajtas.20170602.17
ACS Style
Nicholas Makumi; Romanus Odhiambo; George Otieno Orwa; Stellamaris Adhiambo. On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total. Am. J. Theor. Appl. Stat. 2017, 6(2), 117-122. doi: 10.11648/j.ajtas.20170602.17
AMA Style
Nicholas Makumi, Romanus Odhiambo, George Otieno Orwa, Stellamaris Adhiambo. On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total. Am J Theor Appl Stat. 2017;6(2):117-122. doi: 10.11648/j.ajtas.20170602.17
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Download@article{10.11648/j.ajtas.20170602.17,
author = {Nicholas Makumi and Romanus Odhiambo and George Otieno Orwa and Stellamaris Adhiambo},
title = {On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {2},
pages = {117-122},
doi = {10.11648/j.ajtas.20170602.17},
url = {https://doi.org/10.11648/j.ajtas.20170602.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170602.17},
abstract = {The precision of an estimator is at times discussed regarding the variance. Usually, the exact value of the variance is unknown. The discussion relies on unknown populace quantities. When a researcher obtains the survey data, an estimate of the variance can, therefore, be calculated. When survey results are presented, it is good practice to provide variance estimates for the estimator used in the study. The estimator of the variance can further be used to construct confidence interval, assuming that the sampling distribution of estimator is approximately normal. This study proposes estimation of standard error and confidence interval for a nonparametric regression estimator for a finite population using bootstrapping method. The idea behind bootstrapping is to carry out computations on the collected data. Computation activity assists in estimating the disparity of statistics that are themselves computed from the same data. The variance of the Nadaraya-Watson estimator is derived, based on bootstrap procedure. This operation has led to the derivation of confidence interval associated with Nadaraya-Watson estimator of the population total. A simulation study has been carried out. The overall conclusion is that the confidence interval associated with Nadaraya-Watson estimator is tighter than all the other estimators (Horvitz-Thompson estimator, Local linear estimator, and Ratio estimator).},
year = {2017}
}
TY - JOUR T1 - On Bootstrap Confidence Intervals Associated with Nonparametric Regression Estimators for A Finite Population Total AU - Nicholas Makumi AU - Romanus Odhiambo AU - George Otieno Orwa AU - Stellamaris Adhiambo Y1 - 2017/03/21 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.20170602.17 DO - 10.11648/j.ajtas.20170602.17 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 - 117 EP - 122 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20170602.17 AB - The precision of an estimator is at times discussed regarding the variance. Usually, the exact value of the variance is unknown. The discussion relies on unknown populace quantities. When a researcher obtains the survey data, an estimate of the variance can, therefore, be calculated. When survey results are presented, it is good practice to provide variance estimates for the estimator used in the study. The estimator of the variance can further be used to construct confidence interval, assuming that the sampling distribution of estimator is approximately normal. This study proposes estimation of standard error and confidence interval for a nonparametric regression estimator for a finite population using bootstrapping method. The idea behind bootstrapping is to carry out computations on the collected data. Computation activity assists in estimating the disparity of statistics that are themselves computed from the same data. The variance of the Nadaraya-Watson estimator is derived, based on bootstrap procedure. This operation has led to the derivation of confidence interval associated with Nadaraya-Watson estimator of the population total. A simulation study has been carried out. The overall conclusion is that the confidence interval associated with Nadaraya-Watson estimator is tighter than all the other estimators (Horvitz-Thompson estimator, Local linear estimator, and Ratio estimator). VL - 6 IS - 2 ER -
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