Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model
International Journal of Data Science and Analysis
Volume 5, Issue 2, April 2019, Pages: 18-26
Received: Jan. 1, 2019;
Accepted: Jun. 3, 2019;
Published: Jun. 12, 2019
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Alaa Ahmed Abd Elmegaly, Statistics, Ministry of Higher Education and Scientific Research, Cairo, Egypt
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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.
Constrained Principal Components Analysis, General Linear Model, Principal Component Analysis, Simulation and Application, Stochastic Restricted Principal Components
To cite this article
Alaa Ahmed Abd Elmegaly,
Amendments of a Stochastic Restricted Principal Components Regression Estimator in the Linear Model, International Journal of Data Science and Analysis.
Vol. 5, No. 2,
2019, pp. 18-26.
Copyright © 2019 Authors retain the copyright of this article.
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Yan, X. and Su, X. G. (2009) “Linear Regression Analysis Theory and Computing” World Scientific Publishing Co. Pte. Ltd.
Theil, H. and Goldberger, A. S. (1961) "On Pure and Mixed Statistical Estimation in Economics" International Economic Review, 2, 65-78.
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.
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.
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.
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.
Alheety, M. and Kibria, B. M. (2014) "A Generalized Stochastic Restricted Ridge Regression Estimator" Communications in Statistics Theory and Methods, 43, 4415–4427.
Takane, Y. and Shibayama, T. (1991) "Principal Component Analysis With External Information on Both cases and Variables" Psychometrica Mcgill University, 56, 97 -120.
Takane, Y. (2014) "Constrained Principal Component Analysis and Related Techniques" CRC Press Taylor and Francis Group.
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.