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A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations

Author

Listed:
  • Mohammad Arashi

    (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad P.O. Box 9177948974, Iran
    Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Mina Norouzirad

    (Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 3619995181, Iran)

  • Mahdi Roozbeh

    (Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan P.O. Box 3514799422, Iran)

  • Naushad Mamode Khan

    (Department of Economics and Statistics, University of Mauritius, Réduit 80837, Mauritius)

Abstract

The ridge regression estimator is a commonly used procedure to deal with multicollinear data. This paper proposes an estimation procedure for high-dimensional multicollinear data that can be alternatively used. This usage gives a continuous estimate, including the ridge estimator as a particular case. We study its asymptotic performance for the growing dimension, i.e., p → ∞ when n is fixed. Under some mild regularity conditions, we prove the proposed estimator’s consistency and derive its asymptotic properties. Some Monte Carlo simulation experiments are executed in their performance, and the implementation is considered to analyze a high-dimensional genetic dataset.

Suggested Citation

  • Mohammad Arashi & Mina Norouzirad & Mahdi Roozbeh & Naushad Mamode Khan, 2021. "A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3057-:d:690057
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    References listed on IDEAS

    as
    1. Sill, Martin & Hielscher, Thomas & Becker, Natalia & Zucknick, Manuela, 2014. "c060: Extended Inference with Lasso and Elastic-Net Regularized Cox and Generalized Linear Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i05).
    2. Luo, June, 2010. "The discovery of mean square error consistency of a ridge estimator," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 343-347, March.
    3. Amini, Morteza & Roozbeh, Mahdi, 2015. "Optimal partial ridge estimation in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 26-40.
    4. Fikri Akdeniz & Mahdi Roozbeh, 2019. "Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models," Statistical Papers, Springer, vol. 60(5), pages 1717-1739, October.
    Full references (including those not matched with items on IDEAS)

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