Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers

George Kemboi Kirui Keitany; Ananda Omutokoh Kube; Joseph Mutua Mutisya; Fundi Daniel Muriithi

doi:doi:10.11648/j.ajtas.20180704.14

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Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers

George Kemboi Kirui Keitany, Ananda Omutokoh Kube, Joseph Mutua Mutisya, Fundi Daniel Muriithi

Published in American Journal of Theoretical and Applied Statistics (Volume 7, Issue 4)

Received: 17 April 2018 Accepted: 29 May 2018 Published: 29 June 2018

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Abstract

This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.

Published in	American Journal of Theoretical and Applied Statistics (Volume 7, Issue 4)
DOI	10.11648/j.ajtas.20180704.14
Page(s)	156-162
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), 2018. Published by Science Publishing Group

Keywords

Elastic Net, Multicollinearity, Regularization, Nonlinear Least Trimmed Squares, Outliers

References

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George Kemboi Kirui Keitany, Ananda Omutokoh Kube, Joseph Mutua Mutisya, Fundi Daniel Muriithi. (2018). Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. American Journal of Theoretical and Applied Statistics, 7(4), 156-162. https://doi.org/10.11648/j.ajtas.20180704.14

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ACS Style

George Kemboi Kirui Keitany; Ananda Omutokoh Kube; Joseph Mutua Mutisya; Fundi Daniel Muriithi. Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. Am. J. Theor. Appl. Stat. 2018, 7(4), 156-162. doi: 10.11648/j.ajtas.20180704.14

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AMA Style

George Kemboi Kirui Keitany, Ananda Omutokoh Kube, Joseph Mutua Mutisya, Fundi Daniel Muriithi. Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. Am J Theor Appl Stat. 2018;7(4):156-162. doi: 10.11648/j.ajtas.20180704.14

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@article{10.11648/j.ajtas.20180704.14,
  author = {George Kemboi Kirui Keitany and Ananda Omutokoh Kube and Joseph Mutua Mutisya and Fundi Daniel Muriithi},
  title = {Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {4},
  pages = {156-162},
  doi = {10.11648/j.ajtas.20180704.14},
  url = {https://doi.org/10.11648/j.ajtas.20180704.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180704.14},
  abstract = {This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.},
 year = {2018}
}

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TY  - JOUR
T1  - Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers
AU  - George Kemboi Kirui Keitany
AU  - Ananda Omutokoh Kube
AU  - Joseph Mutua Mutisya
AU  - Fundi Daniel Muriithi
Y1  - 2018/06/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180704.14
DO  - 10.11648/j.ajtas.20180704.14
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  - 156
EP  - 162
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180704.14
AB  - This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.
VL  - 7
IS  - 4
ER  -

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Author Information

George Kemboi Kirui Keitany

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Ananda Omutokoh Kube

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Joseph Mutua Mutisya

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Fundi Daniel Muriithi

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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Plain Text BibTeX RIS

APA Style

George Kemboi Kirui Keitany, Ananda Omutokoh Kube, Joseph Mutua Mutisya, Fundi Daniel Muriithi. (2018). Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. American Journal of Theoretical and Applied Statistics, 7(4), 156-162. https://doi.org/10.11648/j.ajtas.20180704.14

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ACS Style

George Kemboi Kirui Keitany; Ananda Omutokoh Kube; Joseph Mutua Mutisya; Fundi Daniel Muriithi. Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. Am. J. Theor. Appl. Stat. 2018, 7(4), 156-162. doi: 10.11648/j.ajtas.20180704.14

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AMA Style

George Kemboi Kirui Keitany, Ananda Omutokoh Kube, Joseph Mutua Mutisya, Fundi Daniel Muriithi. Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers. Am J Theor Appl Stat. 2018;7(4):156-162. doi: 10.11648/j.ajtas.20180704.14

Copy | Download

@article{10.11648/j.ajtas.20180704.14,
  author = {George Kemboi Kirui Keitany and Ananda Omutokoh Kube and Joseph Mutua Mutisya and Fundi Daniel Muriithi},
  title = {Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {7},
  number = {4},
  pages = {156-162},
  doi = {10.11648/j.ajtas.20180704.14},
  url = {https://doi.org/10.11648/j.ajtas.20180704.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20180704.14},
  abstract = {This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Regularized Nonlinear Least Trimmed Squares Estimator in the Presence of Multicollinearity and Outliers
AU  - George Kemboi Kirui Keitany
AU  - Ananda Omutokoh Kube
AU  - Joseph Mutua Mutisya
AU  - Fundi Daniel Muriithi
Y1  - 2018/06/29
PY  - 2018
N1  - https://doi.org/10.11648/j.ajtas.20180704.14
DO  - 10.11648/j.ajtas.20180704.14
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  - 156
EP  - 162
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20180704.14
AB  - This study proposes a regularized robust Nonlinear Least Trimmed squares estimator that relies on an Elastic net penalty in nonlinear regression. Regularization parameter selection was done using a robust cross-validation criterion and estimation through Newton Raphson iteration algorthm for the oprimal model coefficients. Monte Carlo simulation was conducted to verify the theoretical properties outlined in the methodology both for scenarios of presence and absence of multicollinearity and existence of outliers. The proposed procedure performed well compared to the NLS and NLTS in a viewpoint of yielding relatively lower values of MSE and Bias. Furthermore, a real data analysis demonstrated satisfactory performance of the suggested technique.
VL  - 7
IS  - 4
ER  -

Copy | Download