Spline Regression in the Estimation of the Finite Population Total

Joseph Kipyegon Cheruiyot

doi:doi:10.11648/j.sjams.20150305.11

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Spline Regression in the Estimation of the Finite Population Total

Joseph Kipyegon Cheruiyot

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 5)

Received: 10 August 2015 Accepted: 20 August 2015 Published: 2 September 2015

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Abstract

This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 5)
DOI	10.11648/j.sjams.20150305.11
Page(s)	214-224
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

Keywords

Homoscedasticity, Population, Sample, Spline Regression, Robustness, Smoothing, Estimator

References

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APA Style

Joseph Kipyegon Cheruiyot. (2015). Spline Regression in the Estimation of the Finite Population Total. Science Journal of Applied Mathematics and Statistics, 3(5), 214-224. https://doi.org/10.11648/j.sjams.20150305.11

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ACS Style

Joseph Kipyegon Cheruiyot. Spline Regression in the Estimation of the Finite Population Total. Sci. J. Appl. Math. Stat. 2015, 3(5), 214-224. doi: 10.11648/j.sjams.20150305.11

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AMA Style

Joseph Kipyegon Cheruiyot. Spline Regression in the Estimation of the Finite Population Total. Sci J Appl Math Stat. 2015;3(5):214-224. doi: 10.11648/j.sjams.20150305.11

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@article{10.11648/j.sjams.20150305.11,
  author = {Joseph Kipyegon Cheruiyot},
  title = {Spline Regression in the Estimation of the Finite Population Total},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {5},
  pages = {214-224},
  doi = {10.11648/j.sjams.20150305.11},
  url = {https://doi.org/10.11648/j.sjams.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150305.11},
  abstract = {This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.},
 year = {2015}
}

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TY  - JOUR
T1  - Spline Regression in the Estimation of the Finite Population Total
AU  - Joseph Kipyegon Cheruiyot
Y1  - 2015/09/02
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150305.11
DO  - 10.11648/j.sjams.20150305.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 214
EP  - 224
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150305.11
AB  - This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.
VL  - 3
IS  - 5
ER  -

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Author Information

Joseph Kipyegon Cheruiyot

Department of Computer and Statistics, Moi University, Eldoret, Kenya

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APA Style

Joseph Kipyegon Cheruiyot. (2015). Spline Regression in the Estimation of the Finite Population Total. Science Journal of Applied Mathematics and Statistics, 3(5), 214-224. https://doi.org/10.11648/j.sjams.20150305.11

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ACS Style

Joseph Kipyegon Cheruiyot. Spline Regression in the Estimation of the Finite Population Total. Sci. J. Appl. Math. Stat. 2015, 3(5), 214-224. doi: 10.11648/j.sjams.20150305.11

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AMA Style

Joseph Kipyegon Cheruiyot. Spline Regression in the Estimation of the Finite Population Total. Sci J Appl Math Stat. 2015;3(5):214-224. doi: 10.11648/j.sjams.20150305.11

Copy | Download

@article{10.11648/j.sjams.20150305.11,
  author = {Joseph Kipyegon Cheruiyot},
  title = {Spline Regression in the Estimation of the Finite Population Total},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {3},
  number = {5},
  pages = {214-224},
  doi = {10.11648/j.sjams.20150305.11},
  url = {https://doi.org/10.11648/j.sjams.20150305.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150305.11},
  abstract = {This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Spline Regression in the Estimation of the Finite Population Total
AU  - Joseph Kipyegon Cheruiyot
Y1  - 2015/09/02
PY  - 2015
N1  - https://doi.org/10.11648/j.sjams.20150305.11
DO  - 10.11648/j.sjams.20150305.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 214
EP  - 224
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20150305.11
AB  - This study sought to estimate finite population total using Spline regression function. It compared the Spline regression with Sample Mean estimator, design-based and model - based estimators. To measure the performance of each estimator, the study considered average bias, the efficiency by use of the mean square error and the robustness using the rate change of efficiency. In this research, five populations were used. Three of them were simulated according to the following models: linear homoscedastic, quadratic homoscedastic and linear heteroscedastic and two natural populations. The performances of the five estimators were studied under the five populations. The sudy found that Sample Mean(SM), Horvitz-Thompson (HT) and Ratio (R) estimators are not robust while Nadaraya-Watson(NW) and Periodic Spline(PS) are robust when linearity and homoscedasticity of the population structure are violated.
VL  - 3
IS  - 5
ER  -

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