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

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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[12] Park, H. (2013). Robust regression modelling via l1 type regularization. Dept. of Mathematics Chuo University.
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[14] Sima, D. (Apr. 2006). Regularization techniques in modeling and parameter estimation. PhD thesis.
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[16] Tateishi, S., Matsui, H., and Konishi, S. (2009). Nonlinear regression via the lasso-type regularization. Journal of statistical planning and inference.
[17] Tikhonov, A. N. (1943). On the stability of inverse problems. Dokl. Akad. Nauk SSSR, 39:176-179.
[18] Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, B67: 301-320.
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Cite This Article
  • 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

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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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    AU  - Ananda Omutokoh Kube
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    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.
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Author Information
  • Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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

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

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

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