Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model

Alaa Ahmed Abd Elmegaly

doi:doi:10.11648/j.ijdsa.20190502.12

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Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model

Alaa Ahmed Abd Elmegaly

Published in International Journal of Data Science and Analysis (Volume 5, Issue 2)

Received: 1 January 2019 Accepted: 3 June 2019 Published: 12 June 2019

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Abstract

Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix T_r) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 2)
DOI	10.11648/j.ijdsa.20190502.12
Page(s)	18-26
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

Constrained Principal Components Analysis, General Linear Model, Principal Component Analysis, Simulation and Application, Stochastic Restricted Principal Components

References

[1]	Yan, X. and Su, X. G. (2009) “Linear Regression Analysis Theory and Computing” World Scientific Publishing Co. Pte. Ltd.
[2]	Theil, H. and Goldberger, A. S. (1961) "On Pure and Mixed Statistical Estimation in Economics" International Economic Review, 2, 65-78.
[3]	He, D. and Wu, Y. (2014) “A Stochastic Restricted Principal Components Regression Estimator in the Linear Model” Hindawi Publishing Corporation the Scientific World Journal. http://dx.doi.org/10.1155/2014/231506.
[4]	Abd Elmegaly, A. A. (2019) "Statistical Inference of Constrained principal components Models" unpublished Ph. D. thesis, faculty of graduate studies for statistical studies- Cairo University- Egypt.
[5]	Tamura, R., Kobayashi, K., Takano, Y., Miyashiro, R., Nakata, K., and Matsui, T. (2019) "Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor" Journal of Global Optimization, 73, 431-446.
[6]	Batah, M. Özkale, M. and Gore, S. (2009) "Combining Unbiasd Ridge and Principal Component Regression Estimators" Communications in Statistics - Theory and Methods, 38, 2201–2209.
[7]	Alheety, M. and Kibria, B. M. (2014) "A Generalized Stochastic Restricted Ridge Regression Estimator" Communications in Statistics Theory and Methods, 43, 4415–4427.
[8]	Takane, Y. and Shibayama, T. (1991) "Principal Component Analysis With External Information on Both cases and Variables" Psychometrica Mcgill University, 56, 97 -120.
[9]	Takane, Y. (2014) "Constrained Principal Component Analysis and Related Techniques" CRC Press Taylor and Francis Group.
[10]	Rady, E. A., Mohamed, S. M., and Abd Elmegaly, A. A. (2018) “Statistical analysis of the count and profitability of air conditioners” Data in Brief, 19, 413-423. https://doi.org/10.1016/j.dib.2018.05.035.

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Alaa Ahmed Abd Elmegaly. (2019). Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. International Journal of Data Science and Analysis, 5(2), 18-26. https://doi.org/10.11648/j.ijdsa.20190502.12

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ACS Style

Alaa Ahmed Abd Elmegaly. Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. Int. J. Data Sci. Anal. 2019, 5(2), 18-26. doi: 10.11648/j.ijdsa.20190502.12

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AMA Style

Alaa Ahmed Abd Elmegaly. Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. Int J Data Sci Anal. 2019;5(2):18-26. doi: 10.11648/j.ijdsa.20190502.12

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@article{10.11648/j.ijdsa.20190502.12,
  author = {Alaa Ahmed Abd Elmegaly},
  title = {Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {2},
  pages = {18-26},
  doi = {10.11648/j.ijdsa.20190502.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190502.12},
  abstract = {Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix Tr) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.},
 year = {2019}
}

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TY  - JOUR
T1  - Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model
AU  - Alaa Ahmed Abd Elmegaly
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190502.12
DO  - 10.11648/j.ijdsa.20190502.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 18
EP  - 26
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190502.12
AB  - Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix Tr) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.
VL  - 5
IS  - 2
ER  -

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Author Information

Alaa Ahmed Abd Elmegaly

Statistics, Ministry of Higher Education and Scientific Research, Cairo, Egypt

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APA Style

Alaa Ahmed Abd Elmegaly. (2019). Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. International Journal of Data Science and Analysis, 5(2), 18-26. https://doi.org/10.11648/j.ijdsa.20190502.12

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ACS Style

Alaa Ahmed Abd Elmegaly. Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. Int. J. Data Sci. Anal. 2019, 5(2), 18-26. doi: 10.11648/j.ijdsa.20190502.12

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AMA Style

Alaa Ahmed Abd Elmegaly. Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model. Int J Data Sci Anal. 2019;5(2):18-26. doi: 10.11648/j.ijdsa.20190502.12

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@article{10.11648/j.ijdsa.20190502.12,
  author = {Alaa Ahmed Abd Elmegaly},
  title = {Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {2},
  pages = {18-26},
  doi = {10.11648/j.ijdsa.20190502.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190502.12},
  abstract = {Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix Tr) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model
AU  - Alaa Ahmed Abd Elmegaly
Y1  - 2019/06/12
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdsa.20190502.12
DO  - 10.11648/j.ijdsa.20190502.12
T2  - International Journal of Data Science and Analysis
JF  - International Journal of Data Science and Analysis
JO  - International Journal of Data Science and Analysis
SP  - 18
EP  - 26
PB  - Science Publishing Group
SN  - 2575-1891
UR  - https://doi.org/10.11648/j.ijdsa.20190502.12
AB  - Principal component Analysis (PCA) is one of the popular methods used to solve the multicollinearity problem. Researchers in 2014 proposed an estimator to solve this problem in the linear model when there were stochastic linear restrictions on the regression coefficients. This estimator was called the stochastic restricted principal components (SRPC) regression estimator. The estimator was constructed by combining the ordinary mixed estimator (OME) and the principal components regression (PCR) estimator. It ignores the number of components (orthogonal matrix Tr) that the researchers choose to solve the multicollinearity problem in the data matrix (X). This paper proposed four different methods (Lagrange function, the same technique, the constrained principal component model, and substitute in model) to modify the (SRPC) estimator to be used in case of multicollinearity. Finally, a numerical example, an application, and simulation study have been introduced to illustrate the performance of the proposed estimator.
VL  - 5
IS  - 2
ER  -

Copy | Download