A nonlinear mixed–integer programming approach for variable selection in linear regression model

References

• Akdenïz Duran, E., W. K. Härdle, and M. Osipenko. 2012. Difference based ridge and Liu type estimators in semiparametric regression models. Journal of Multivariate Analysis 105 (1):164–75. doi:10.1016/j.jmva.2011.08.018.
   Web of Science ®Google Scholar
• Akdeniz, F., and Roozbeh, M. 2019. Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models. Statistical Papers 60:1717–1739.
   Google Scholar
• Akdenïz, F., and G. Tabakan. 2009. Restricted ridge estimators of the parameters in semiparametric regression model. Communications in Statistics—Theory and Methods 38:1852–69.
   Web of Science ®Google Scholar
• Arashi, M., and M. Roozbeh. 2019. Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data. Statistical Papers 60:667–686.
   Google Scholar
• Arashi, M.,M. Roozbeh, N. A. Hamzah, and M. Gasparini. 2021. Robust ridge regression and its applications in genetic studies. PLOS ONE 16, e0245376.
   Google Scholar
• Babaie-Kafaki, S., and Roozbeh, M. 2017. A revised Cholesky decomposition to combat multicollinearity inmultiple regression models, Journal of Statistical Computation & Simulation 87, 2298–2308.
   Google Scholar
• Bertsimas, D., and J. N. Tsitsiklis. 1997. Introduction to linear optimization. Belmont, MA: Athena Scientific.
   Google Scholar
• Bühlmann, P., M. Kalisch, and L. Meier. 2014. High–dimensional statistics with a view towards applications in biology. Annual Review of Statistics and Its Application 1 (1):255–78. doi:10.1146/annurev-statistics-022513-115545.
   Web of Science ®Google Scholar
• Fallah, R., M. Arashi, and S. M. M. Tabatabaey. 2017. On the ridge regression estimator with sub-space restriction. Communications in Statistics - Theory and Methods 46 (23):11854–65. doi:10.1080/03610926.2017.1285928.
   Web of Science ®Google Scholar
• Fan, J., and H. Peng. 2004. penalized likelihood with a diverging number of parameters. The Annals of Statistics 32 (3):928–61. doi:10.1214/009053604000000256.
   Web of Science ®Google Scholar
• Gibbons, D. G. 1981. A simulation study of some ridge estimators. Journal of the American Statistical Association 76:131–9.
   Web of Science ®Google Scholar
• Hassanzadeh Bashtian, M., M. Arashi, and S. M. M. Tabatabaey. 2011. Ridge estimation under the stochastic restriction. Communications in Statistics - Theory and Methods 40 (21):3711–47. doi:10.1080/03610926.2010.494809.
   Web of Science ®Google Scholar
• Kibria, B. M. G. 2012. Some Liu and ridge type estimators and their properties under the ill-conditioned gaussian linear regression model. Journal of Statistical Computation and Simulation 82 (1):1–17. doi:10.1080/00949655.2010.519705.
   Web of Science ®Google Scholar
• McDonald, G. C., and D. I. Galarneau. 1975. A Monte Carlo evaluation of some ridge–type estimators. Journal of the American Statistical Association 70 (350):407–16. doi:10.1080/01621459.1975.10479882.
   Web of Science ®Google Scholar
• Meinshausen, N., L. Meier, and P. Bühlmann. 2009. p–values for high–dimensional regression. Journal of the American Statistical Association 104 (488):1671–81. doi:10.1198/jasa.2009.tm08647.
   Web of Science ®Google Scholar
• Najarian, S., M. Arashi, and B. M. G. Kibria. 2013. A simulation study on some restricted ridge regression estimators. Communications in Statistics - Simulation and Computation 42 (4):871–9. doi:10.1080/03610918.2012.659953.
   Web of Science ®Google Scholar
• Roozbeh, M. 2015. Shrinkage ridge estimators in semiparametric regression models. Journal of Multivariate Analysis 136:56–74. doi:10.1016/j.jmva.2015.01.002.
   Web of Science ®Google Scholar
• Roozbeh, M. 2018. Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion. Computational Statistics & Data Analysis 117: 45–61.
   Google Scholar
• Roozbeh, M.,S. Babaie-Kafaki, and A. NaeimiSadigh.2018. A heuristic approach to combat multicollinearity in least trimmed squares regression analysis. Applied Mathematical Modelling 57: 105–120.
   Google Scholar
• Roozbeh, M.,S. Babaie-Kafaki, and Z. Aminifard. 2021. Two penalized mixed-integer nonlinear programming approaches to tackle multicollinearity and outliers effects in linear regression models. Journal of Industrial & Management Optimization 17, 3475–3491.
   Google Scholar
• Shao, J., and X. Deng. 2012. Estimation in high–dimensional linear models with deterministic design matrices. The Annals of Statistics 40 (2):812–31. doi:10.1214/12-AOS982.
   Web of Science ®Google Scholar
• Tabakan, G., and F. Akdenïz. 2010. Difference-based ridge estimator of parameters in partial linear model. Statistical Papers 51 (2):357–68. doi:10.1007/s00362-008-0192-6.
   Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B (Methodological) 58:267–88.
   Web of Science ®Google Scholar
• Wang, H. 2009. Forward regression for ultra–high dimensional variable screening. Journal of the American Statistical Association 104 (488):1512–24. doi:10.1198/jasa.2008.tm08516.
   Web of Science ®Google Scholar
• Yüzbaşi, B., and M. Arashi. 2019. Double shrunken selection operator. Communications in Statistics - Simulation and Computation 48 (3):666–74. doi:10.1080/03610918.2017.1395040.
   Web of Science ®Google Scholar
• Yüzbaşi, B., M. Arashi, and S. E. Ahmed. 2020. Shrinkage estimation strategies in generalized ridge regression models under low/high-dimension regime. International Statistical Review 88 (1):229–51. doi:10.1111/insr.12351.
   Web of Science ®Google Scholar
• Yüzbaşi, B., M. Arashi, and F. Akdeniz. 2021. Penalized regression via the restricted bridge estimator. Soft Computing 25 (13):8401–16. doi:10.1007/s00500-021-05763-9.
   Web of Science ®Google Scholar
• Zhang, C. H. 2010. Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics 38 (2):894–942. doi:10.1214/09-AOS729.
   Web of Science ®Google Scholar
• Zhang, C. H., and J. Huang. 2008. The sparsity and bias of the LASSO selection in high–dimensional linear regression. The Annals of Statistics 36 (4):1567–94. doi:10.1214/07-AOS520.
   Web of Science ®Google Scholar