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Article

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

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Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad P.O. Box 9177948974, Iran
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Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
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Department of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 3619995181, Iran
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Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan P.O. Box 3514799422, Iran
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Department of Economics and Statistics, University of Mauritius, Réduit 80837, Mauritius
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Author to whom correspondence should be addressed.
Academic Editor: Jin-Ting Zhang
Mathematics 2021, 9(23), 3057; https://doi.org/10.3390/math9233057
Received: 10 November 2021 / Revised: 23 November 2021 / Accepted: 24 November 2021 / Published: 28 November 2021
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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. View Full-Text
Keywords: asymptotic; high–dimension; Liu estimator; multicollinear; ridge estimator asymptotic; high–dimension; Liu estimator; multicollinear; ridge estimator
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MDPI and ACS Style

Arashi, M.; Norouzirad, M.; Roozbeh, M.; Khan, N.M. A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations. Mathematics 2021, 9, 3057. https://doi.org/10.3390/math9233057

AMA Style

Arashi M, Norouzirad M, Roozbeh M, Khan NM. A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations. Mathematics. 2021; 9(23):3057. https://doi.org/10.3390/math9233057

Chicago/Turabian Style

Arashi, Mohammad, Mina Norouzirad, Mahdi Roozbeh, and Naushad Mamode Khan. 2021. "A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations" Mathematics 9, no. 23: 3057. https://doi.org/10.3390/math9233057

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