Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms

Yafeng Xia; Lin Yan

doi:doi:10.11648/j.ijsd.20220801.12

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Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms

Yafeng Xia, Lin Yan

Published in International Journal of Statistical Distributions and Applications (Volume 8, Issue 1)

Received: 17 March 2022 Accepted: 6 April 2022 Published: 23 April 2022

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Abstract

Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.

Published in	International Journal of Statistical Distributions and Applications (Volume 8, Issue 1)
DOI	10.11648/j.ijsd.20220801.12
Page(s)	14-23
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), 2024. Published by Science Publishing Group

Keywords

Profile Forward Selection, Strong Genetic Condition, Marginality Principle, Screening Consistency, Variable Selection

References

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APA Style

Yafeng Xia, Lin Yan. (2022). Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. International Journal of Statistical Distributions and Applications, 8(1), 14-23. https://doi.org/10.11648/j.ijsd.20220801.12

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ACS Style

Yafeng Xia; Lin Yan. Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. Int. J. Stat. Distrib. Appl. 2022, 8(1), 14-23. doi: 10.11648/j.ijsd.20220801.12

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AMA Style

Yafeng Xia, Lin Yan. Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. Int J Stat Distrib Appl. 2022;8(1):14-23. doi: 10.11648/j.ijsd.20220801.12

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@article{10.11648/j.ijsd.20220801.12,
  author = {Yafeng Xia and Lin Yan},
  title = {Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {1},
  pages = {14-23},
  doi = {10.11648/j.ijsd.20220801.12},
  url = {https://doi.org/10.11648/j.ijsd.20220801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220801.12},
  abstract = {Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.},
 year = {2022}
}

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TY  - JOUR
T1  - Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms
AU  - Yafeng Xia
AU  - Lin Yan
Y1  - 2022/04/23
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220801.12
DO  - 10.11648/j.ijsd.20220801.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 14
EP  - 23
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220801.12
AB  - Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.
VL  - 8
IS  - 1
ER  -

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Author Information

Yafeng Xia

School of Sciences, Lanzhou University of Technology, Department of University, Lanzhou, China
Lin Yan

School of Sciences, Lanzhou University of Technology, Department of University, Lanzhou, China

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Plain Text BibTeX RIS

APA Style

Yafeng Xia, Lin Yan. (2022). Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. International Journal of Statistical Distributions and Applications, 8(1), 14-23. https://doi.org/10.11648/j.ijsd.20220801.12

Copy | Download

ACS Style

Yafeng Xia; Lin Yan. Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. Int. J. Stat. Distrib. Appl. 2022, 8(1), 14-23. doi: 10.11648/j.ijsd.20220801.12

Copy | Download

AMA Style

Yafeng Xia, Lin Yan. Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms. Int J Stat Distrib Appl. 2022;8(1):14-23. doi: 10.11648/j.ijsd.20220801.12

Copy | Download

@article{10.11648/j.ijsd.20220801.12,
  author = {Yafeng Xia and Lin Yan},
  title = {Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms},
  journal = {International Journal of Statistical Distributions and Applications},
  volume = {8},
  number = {1},
  pages = {14-23},
  doi = {10.11648/j.ijsd.20220801.12},
  url = {https://doi.org/10.11648/j.ijsd.20220801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20220801.12},
  abstract = {Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Variable Selection Based on Profile Forward Selection of Partial Linear Models with Interactive Terms
AU  - Yafeng Xia
AU  - Lin Yan
Y1  - 2022/04/23
PY  - 2022
N1  - https://doi.org/10.11648/j.ijsd.20220801.12
DO  - 10.11648/j.ijsd.20220801.12
T2  - International Journal of Statistical Distributions and Applications
JF  - International Journal of Statistical Distributions and Applications
JO  - International Journal of Statistical Distributions and Applications
SP  - 14
EP  - 23
PB  - Science Publishing Group
SN  - 2472-3509
UR  - https://doi.org/10.11648/j.ijsd.20220801.12
AB  - Due to the rapid development of information technology and data acquisition technology, the model which only considers the linear main effect can not provide accurate prediction results, and the interaction between the predictor and response variables can not be ignored, so the variable selection problem of the model with interaction terms has become an important research topic in the statistical analysis today. In this paper, we discuss the problem of variable selection for a partially linear model with interaction terms using the profile forward selection method under high dimensional data. We propose the two-stage interactive selection algorithm (iPFST) under strong genetic condition and the profile forward selection algorithm (iPFSM) under marginality principle respectively. Theoretically, we use the consistency of profile estimators to prove that profile estimators have uniform convergence rate, and use the screening consistency to prove that iPFST algorithm and iPFSM algorithm can uniformly identify all important linear main effect terms and important interaction effect terms with probability 1. Seven regularization conditions for the theorem are given. Numerical simulation shows the superiority of iPFST and iPFSM in variable selection, and the two algorithms are compared, then iPFST algorithm is better than iPFSM algorithm. Finally, we give detailed technical proof.
VL  - 8
IS  - 1
ER  -

Copy | Download