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

Mohammad Arashi, Mina Norouzirad, Mahdi Roozbeh and Naushad Mamode Khan
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Mohammad Arashi: Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad P.O. Box 9177948974, Iran
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

Mathematics, 2021, vol. 9, issue 23, 1-11

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.

Keywords: asymptotic; high–dimension; Liu estimator; multicollinear; ridge estimator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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