Genetic Algorithm in the Wavelet Domain for Large p Small n Regression

References

• Bhandarkar, S., Zhang, Y., Potter, W. (1994). An edge detection technique using genetic algorithm-based optimization. Pattern Recognition 27:1159–1180.
   Web of Science ®Google Scholar
• Boyce, D.E., Fahri, A., Weischedel, R. (1974). Optimal Subset Selection: Multiple Regression, Interdependence, and Optimal Network Algorithms. New York: Springer-Verlag.
   Google Scholar
• Bozdogan, H. (1987). Model selection and Akaike’s information criteria (AIC): the general theory and its analytical extensions. Psychometrica 52:317–332.
   Web of Science ®Google Scholar
• Brown, P.J., Fearn, T., Vannucci, M. (2001). Bayesian wavelet regression on curves with application to a spectroscopic calibration problem. Journal of the American Statistical Association 96(454):398–408.
   Web of Science ®Google Scholar
• Brown, P.J., Vannucci, M., Fearn, T. (1998a). Bayesian wavelength selection in multicomponent analysis. Journal of Chemometrics 12:173–182.
   Web of Science ®Google Scholar
• Brown, P.J., Vannucci, M., Fearn, T. (1998b). Multivariate Bayesian variable selection and prediction. Journal of the Royal Statistical Society: Series B 60(3):627–641.
   Google Scholar
• Brown, P.J., Vannucci, M., Fearn, T. (1999). The choice of variables in multivariate regression: A Bayesian non-conjugate decision theory approach. Biometrika 86:635–648.
   Web of Science ®Google Scholar
• Burns, P. (1992). A Genetic Algorithm for Robust Regression Estimation. Statsci Technical Report. Seattle, Washington: Statistical Sciences, Inc.
   Google Scholar
• Cowe, I.A., McNicol, J.W. (1985). The use of principal components in the analysis of near infrared spectra. Applied Spectroscopy 39(2):257–266.
   Web of Science ®Google Scholar
• Donoho, D.L., Johnstone, I.M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81(3):425–455.
   Web of Science ®Google Scholar
• Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D. (1995). Wavelet shrinkage: asymptopia?Journal of Royal Statistical Society B 57(2):301–369.
   Google Scholar
• Fan, J., Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. Statistica Sinica 20:101–148.
   PubMed Web of Science ®Google Scholar
• George, E.I. (2000). The variable selection problem. Journal of the American Statistical Association 452:1304–1308.
   Google Scholar
• George, E.I., McCulloch, R.E. (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association 88:881–889.
   Web of Science ®Google Scholar
• Goldberg, D. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Boston, MA: Addison-Wesley Longman Publishing Col, Inc.
   Google Scholar
• Greenshtein, E. (2006). Best subset selection, persistence in high-dimensional statistical learning and optimization under constraint. Annals of Statistics 34:2367–2386.
   Web of Science ®Google Scholar
• Hamada, M., Martz, H., Reese, C., Wilson, A. (2001). Finding near-optimal Bayesian experimental designs via genetic algorithms. The American Statistician 55(3):175–181.
   Web of Science ®Google Scholar
• Hocking, R.R. (1976). A Biometrics Invited Paper. The analysis and selection variables in linear regression. Biometrics 32(1):149.
   Web of Science ®Google Scholar
• Hocking, R.R. (1983). Developments in linear regression methodology: 1959–1982. Technometrics 25:219–230.
   Web of Science ®Google Scholar
• Howe, J.A., Bozdogan, H. (2010). Predictive subset VAR modeling using the genetic algorithm and information complexity. European Journal of Pure and Applied Mathematics 3(3):382–405.
   Google Scholar
• Hrushka, W.R. (1987). Data analysis: Wavelength selection methods. In: Near Infrared Technology in the Agriculture and Food Industries, P. C. Williams, K. H. Norris, Eds. St Paul: AACC, pp. 39–58.
   Google Scholar
• Jolliffe, I.T. (1986). Principle Component Analysis. New York: Springer.
   Google Scholar
• Kuo, L., Mallick, B. (1998). Variable selection for regression models. Sankhyā: The Indian Journal of Statistics, Series B 60:65–81.
   Google Scholar
• Liu, M., Bozdogan, H. (2008). Multivariate regression models with power exponential random errors and subset selection using genetic algorithms with information complexity. European Journal of Pure and Applied Mathematics 1:4–37.
   Google Scholar
• Mallat, S. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:674–693.
   Web of Science ®Google Scholar
• Mantel, N. (1970). Why stepdown procedures in variables selection. Technometrics 12:591–612.
   Web of Science ®Google Scholar
• Meyer, M. (2003). An evolutionary algorithm with applications to statistics. Journal of Computational and Graphical Statistics 12(2):265–281.
   Web of Science ®Google Scholar
• Moses, L.E. (1986). Think and Explain with Statistics. Boston MA: Addison-Wesley Longman Publishing Col, Inc.
   Google Scholar
• Neely, C., Weller, P., Dittmar, R. (1997). Is technical analysis in the foreign exchange market profitable? A genetic programming approach. Journal of Financial and Quantitative Analysis 32(4):405–426.
   Web of Science ®Google Scholar
• Osborne, B.G., Fearn, T., Miller, A.R., Douglas, S. (1984). Application of near- infrared reflectance spectroscopy to compositional analysis of biscuits and biscuit doughs. Journal of the Science of Food and Agriculture 35:99–105.
   Web of Science ®Google Scholar
• Peng, D., Li, X., Dong, K., Zhang, G. (2010). Multivariate analysis of near-infrared spectra by wavelet domain regression using genetic algorithm. SOPO–Symposium on Photonics and Optoelectronics, Cheng du, China, 19–21 June 2010, 936939.
   Google Scholar
• Routledge, B. (1999). Adaptive learning in financial markets. In: The Review of Financial Studies. Vol. 44. Oxford: Oxford University Press, pp. 1165–1202.
   Google Scholar
• Vannucci, M., Brown, P.J., Fearn, T. (2003). A decision theoretical approach to wavelet regression on curves with a high number of regressor. Journal of Statistical Planning and Inference 112:195–212.
   Web of Science ®Google Scholar
• Vidakovic, B. (1999). Statistical Modeling by Wavelets. New York: Wiley.
   Google Scholar
• West, J., Linster, B. (2003). The evolution of Fuzzy rules in two-player games. Southern Economic Journal 69(3):705–717.
   Web of Science ®Google Scholar
• Wilkinson, L. (1989). SYSTAT: The System for Statistics. Evanston, IL: SYSTAT.
   Google Scholar
• Wold, S., Martens, H., Wold, H. (1983). The multivariate calibration problem in chemistry solved by PLS. In: Matrix Pencils, Lecture Notes in Mathematics. (A. Ruhe, B. Kagstrom, eds.). Proceedings of the Conference on Matrix Pencils, Lecture Notes in Mathematics, Heidelberg: Springer, pp. 286–293.
   Google Scholar