A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations
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 cas...
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3057 |
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| author | Mohammad Arashi Mina Norouzirad Mahdi Roozbeh Naushad Mamode Khan |
| author_facet | Mohammad Arashi Mina Norouzirad Mahdi Roozbeh Naushad Mamode Khan |
| author_sort | Mohammad Arashi |
| collection | DOAJ |
| description | 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., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> when <i>n</i> 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. |
| first_indexed | 2024-03-10T04:48:50Z |
| format | Article |
| id | doaj.art-e112f10a0cc248deb93e6478f0a0e09d |
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| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:50Z |
| publishDate | 2021-11-01 |
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| series | Mathematics |
| spelling | doaj.art-e112f10a0cc248deb93e6478f0a0e09d2023-11-23T02:45:23ZengMDPI AGMathematics2227-73902021-11-01923305710.3390/math9233057A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear SituationsMohammad Arashi0Mina Norouzirad1Mahdi Roozbeh2Naushad Mamode Khan3Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad P.O. Box 9177948974, IranDepartment of Statistics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood P.O. Box 3619995181, IranDepartment of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan P.O. Box 3514799422, IranDepartment of Economics and Statistics, University of Mauritius, Réduit 80837, MauritiusThe 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., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> when <i>n</i> 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.https://www.mdpi.com/2227-7390/9/23/3057asymptotichigh–dimensionLiu estimatormulticollinearridge estimator |
| spellingShingle | Mohammad Arashi Mina Norouzirad Mahdi Roozbeh Naushad Mamode Khan A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations Mathematics asymptotic high–dimension Liu estimator multicollinear ridge estimator |
| title | A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations |
| title_full | A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations |
| title_fullStr | A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations |
| title_full_unstemmed | A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations |
| title_short | A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations |
| title_sort | high dimensional counterpart for the ridge estimator in multicollinear situations |
| topic | asymptotic high–dimension Liu estimator multicollinear ridge estimator |
| url | https://www.mdpi.com/2227-7390/9/23/3057 |
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