CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization

References

• Neter, J, Kutner, M, Wasserman, W, and Nachtsheim, C, 1996. Applied Linear Statistical Models. Boston: WCB/McGrawHill; 1996.
   Google Scholar
• Zareipour, H, Bhattacharya, K, and Canizares, CA, 2006. Forecasting the hourly Ontario energy price by multivariate adaptive regression splines. Power Engineering Society General Meeting, IEEE; 2006.
   Google Scholar
• Friedman, JH, 1991. Multivariate adaptive regression splines, Ann. Stat. 19 (1991), pp. 1–141.
   Web of Science ®Google Scholar
• Di, W, 2006. Long Term Fixed Mortgage Rate Prediction Using Multivariate Adaptive Regression Splines. Nanyang: School of Computer Engineering, Nanyang Technological University; 2006.
   Google Scholar
• Zhou, Y, and Leung, H, 2007. Predicting object-oriented software maintainability using multivariate adaptive regression splines, J. Syst. Software 80 (2007), pp. 1349–1361.
   Web of Science ®Google Scholar
• Deconinck, E, Coomons, D, and Heyden, YV, 2007. Explorations of linear modelling techniques and their combinations with multivariate adaptive regression splines to predict gastro-intestinal absorption of drugs, J. Pharma. Biomed. Anal. 43 (2007), pp. 119–130.
   PubMed Web of Science ®Google Scholar
• Tsai, JCC, and Chen, VCP, 2005. Flexible and robust implementations of multivariate adaptive regression splines within a wastewater treatment stochastic dynamic program, Quality Reliability Eng. Int. 21 (2005), pp. 689–699.
   Web of Science ®Google Scholar
• Elith, J, and Leathwick, J, 2007. Predicting species distribution from museum and herbarium records using multiresponse models fitted with multivariate adaptive regression splines, Divers. Distributions 13 (2007), pp. 265–275.
   Web of Science ®Google Scholar
• Haas, H, and Kubin, G, , A multi-band nonlinear oscillator model for speech, Conference Record of the Thirty- Second Asilomar Conference on Signals, Syst. Comput. 1 (1998), pp. 338–342.
   Google Scholar
• Lee, TS, Chiu, CC, Chou, YC, and Lu, CJ, 2006. Mining the customer credit using classification and regression tree and multivariate adaptive regression splines, Comput. Stat. Data Anal. 50 (2006), pp. 1113–1130.
   Web of Science ®Google Scholar
• Chou, SM, Lee, TS, Shao, YE, and Chen, IF, 2004. Mining the breast cancer pattern using artificial neural networks and multivariate adaptive regression splines, Expert Syst. Appl. 27 (2004), pp. 133–142.
   Web of Science ®Google Scholar
• Ko, M, and Bryson, KMO, 2008. Reexamining the impact of information technology investment an productivity using regression tree and multivariate adaptive regression splines (MARS), Information Technol. Manag. 9 (2008), pp. 285–299.
   Web of Science ®Google Scholar
• Breiman, L, Friedman, JH, Olshen, R, and Stone, C, 1984. Classification and Regression Trees. Belmont, CA: Wadsworth; 1984.
   Google Scholar
• Taylan, P, Weber, GW, and Yerlikaya, F, , Continuous optimization applied in MARS for modern applications in finance, science and technology, ISI Proceedings of 20th Mini-EURO Conference Continuous Optimization and Knowledge-Based Technologies, Neringa, Lithuania (2008), pp. 317–322.
   Google Scholar
• Nesterov, YE, and Nemirovski, AS, 1994. Interior Point Polynomial Algorithms in Convex Programming. Philadelphia: SIAM; 1994.
   Google Scholar
• Nemirovski, A, 2002. A Lecture on Modern Convex Optimization. Israel Institute of Technology; 2002, Available at http://iew3.technion.ac.il/Labs/Opt/opt/LN/Final.pdf.
   Google Scholar
• MOSEK, A, , very powerful commercial software for CQP. Available at http://www.mosek.com.
   Google Scholar
• Taylan, P, Weber, GW, and Beck, A, 2007. New approaches to regression by generalized additive models and continuoues optimization for modern applications in finance, science and technology, J. Optim. 56 (2007), pp. 675–698.
   Web of Science ®Google Scholar
• Aster, RC, Borchers, B, and Thurber, C, 2004. Parameter Estimation and Inverse Problems. Burlington, MA: Academic Press; 2004.
   Google Scholar
• Hastie, T, Tibshirani, R, and Friedman, J, 2001. The Elements of Statistical Learning, Data Mining, Inference and Prediction. New York: Springer; 2001.
   Google Scholar
• Ben-Tal, A, 2002. Conic and Robust Optimization, Lecture Notes for the Course. Haifa, Israel: Minerva Optimization Center, Technion Israel Institute of Technology; 2002.
   Google Scholar
• Yerlikaya, F, 2008. A new contribution to nonlinear robust regression and classification with MARS and its application to data mining for quality control in manufacturing. MSc. thesis, Middle East Technical University; 2008.
   Google Scholar
• Myers, RH, and Montgomery, DC, 2002. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. New York: Wiley; 2002.
   Google Scholar
• MARS from Salford Systems, , Available at http://www.salfordsystems.com/mars/phb.
   Google Scholar
• UCI: Machine Learning Repository. Available at http://archive.ics.uci.edu/ml/.
   Google Scholar
• StatLib: Datasets Archive. Available at http://lib.stat.cmu.edu/datasets/.
   Google Scholar
• Kartal, E, 2007. Metamodelling complex systems using liner and nonlinear regression methods. MSc. thesis, Middle East Technical University; 2007.
   Google Scholar
• Bakιr, B, 2006. Defect cause modelling with decision tree and regression analysis: A case study in casting industry. MSc. thesis, Middle East Technical University; 2006.
   Google Scholar
• Martinez, WL, and Martinez, AR, 2002. Computational Statistics Handbook with MATLAB. London: Chapman and Hall, CRC; 2002.
   Google Scholar
• MATLAB Version 7.5 (R2007b).
   Google Scholar
• Davis, CS, 2003. Statistical Methods for the Analysis of Repeated Measures. New York: Springer-Verlag; 2003.
   Google Scholar
• SPSS 16.0 GPL Reference Guide, Chicago, IL: SPSS Inc, 2007. Available at http://support.spss.com/ProductsExt/SPSS/Documentation/SPSSforWindows/.
   Google Scholar
• Jin, R, Chen, W, and Simpson, TW, 2001. Comparative studies of metamodelling techniques under multiple modelling criteria, Struct. Multidisc Optim. 23 (2001), pp. 1–13.
   Web of Science ®Google Scholar
• Hock, W, and Schittkowski, K, 1981. Test Examples for Nonlinear Programming Codes. New York: Springer-Verlag; 1981.
   Google Scholar
• Hansen, PC, 1998. Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. Philadelphia: SIAM; 1998.
   Google Scholar
• Craven, P, and Wahba, G, 1979. Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation, Numer. Math. 31 (1979), pp. 377–403.
   Web of Science ®Google Scholar
• Moisen, GG, and Frescino, TS, 2002. Comparing five modelling techniques for predicting forest characteristics, Ecol. Model. 157 (2002), pp. 209–225.
   Web of Science ®Google Scholar
• Osei-Bryson, KM, 2004. Evaluation of decision trees: A multi-criteria approach, Comput. Oper. Res. 31 (2004), pp. 1933–1945.
   Web of Science ®Google Scholar