Budget constrained model selection for multiple linear regression

References

• Agresti, A. 1996. An Introduction to categorical data analysis. New York: Willey.
   Google Scholar
• Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6):716–23. doi:10.1109/TAC.1974.1100705.
   Web of Science ®Google Scholar
• Bussieck, R. M., and A. Pruessner. 2003. Mixed-integer nonlinear programming. SIAG/OPT Newsletter: Views & News 14:19–22.
   Google Scholar
• Bertsimas, D., and R. Shioda. 2009. Algorithm for cardinality – Constrained quadratic optimization. Computational Optimization and Applications 43 (1):1–22. doi:10.1007/s10589-007-9126-9.
   Web of Science ®Google Scholar
• Bertsimas, D., and A. King. 2016. OR Forum – An algorithmic approach to linear regression. Operations Research 64 (1):2–16. doi:10.1287/opre.2015.1436.
   Web of Science ®Google Scholar
• Bertsimas, D., A. King, and R. Mazumder. 2016. Best subset selection via a modern optimization lens. The Annals of Statistics 44 (2):813–52. doi:10.1214/15-AOS1388.
   Web of Science ®Google Scholar
• Bertsimas, D., and M. Li. 2019. Accounting for significance and multicollinearity in building linear regression models. https://arxiv.org/abs/1712.04543.
   Google Scholar
• Chung, S., Y. W. Park, and T. Cheong. 2017. A mathematical programming approach for integrated multiple linear regression subset selection and validation. https://arxiv.org/abs/1712.04543.
   Google Scholar
• Efroymson, M. A. 1960. Multiple regression analysis. In Mathematical methods for digital computers, eds. A. Ralston and H. S. Wilf, 191–203. New York, NY: Wiley.
   Google Scholar
• Fan, J., and R. Li. 2001. Variable selection via nonconcave penalized likelihood and it s oracle properties. Journal of the American Statistical Association 96 (456):1348–60. doi:10.1198/016214501753382273.
   Web of Science ®Google Scholar
• Fabozzi, F. J., S. M. Focardi, S. T. Rachev, and B. G. Arshanapalli. 2014. The basics of financial econometrics: Tools, concepts, and asset management applications. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Gupta, O. K., and A. Ravindran. 1985. Branch and Bound Experiments in Convex Nonlinear Integer Programming. Management Science 31 (12):1533–46. doi:10.1287/mnsc.31.12.1533.
   Web of Science ®Google Scholar
• Grossmann, I. E., and N. V. Sahinidis. 2002. Prologue. Optimization and Engineering 4 (1–2):5–6.
   Google Scholar
• Kohavi, R., and H. G. John. 1997. Wrappers for feature subset selection. Artificial Intelligence 97 (1-2):273–324. doi:10.1016/S0004-3702(97)00043-X.
   Web of Science ®Google Scholar
• Li, R., and D. J. Lin. 2009. Variable selection for screening experiments. Quality Technology & Quantitative Management 6 (3):271–80.
   PubMed Web of Science ®Google Scholar
• Parpoula, C., K. Drosou, C. Koukouvinos, and K. Mylona. 2021. A new variable selection approach inspired by supersaturated designs given a large-dimensional dataset. Journal of Data Science 12 (1):35–52. doi:10.6339/JDS.201401_12(1).0003.
   Google Scholar
• Park, Y. W., and D. Klabjan. 2017. Subset selection for multiple linear regression via optimization. https://arxiv.org/abs/1701.07920.
   Google Scholar
• Priestley, M. B. 1981. Spectral analysis and time series, 375. Hoboken, NJ: Academic Press.
   Google Scholar
• Rardin, R. L. 2017. Optimization in operations research, 2nd ed. Prentice Hall, NJ: Pearson Education, Inc.
   Google Scholar
• Rejchel, W. 2016. Lasso with convex loss: Model selection consistency and estimation. Communications in Statistics – Theory and Methods 45 (7):1989–2004. doi:10.1080/03610926.2013.870799.
   Web of Science ®Google Scholar
• Scott, M. 2004. Six approaches to calculating standardized logistic regression coefficients. The American Statistician 58 (3):218–23.
   Web of Science ®Google Scholar
• Tibshirani, R. 1996. Regression shrinkage and selection via the Lasso. J. Roy. Sat. Soc 58:267–88.
   Google Scholar
• Tamura, R., K. Kobayashi, Y. Takano, R. Miyashiro, K. Nakata, and T. Matsui. 2019. Mixed integer quadratic optimization formulations for eliminating multicollinearity based on variance inflation factor. Journal of Global Optimization 73 (2):431–46. doi:10.1007/s10898-018-0713-3.
   Web of Science ®Google Scholar
• Wu, J., L. Xue, and P. Zhao. 2018. Quickly variable selection for varying coefficient models with missing response at random. Communications in Statistics – Theory and Methods 47 (10):2327–36. doi:10.1080/03610926.2014.922989.
   Web of Science ®Google Scholar
• Yamada, S. 2004. Selection of active factors by stepwise regression in the data analysis of supersaturated design. Quality Engineering 16 (4):501–13. doi:10.1081/QEN-120038012.
   Google Scholar