Variable selection in regression using maximal correlation and distance correlation

References

• Rényi A. On measures of dependence. Acta Math Acad Sci Hungar. 1959;10:441–451. doi: 10.1007/BF02024507
   Google Scholar
• Sakamoto Y, Ishiguro M, Kitagawa G. Akaike information criterion statistics. Tokyo: D. Reidel; 1986.
   Google Scholar
• Schwarz G. Estimating the dimension of a model. Ann Stat. 1978;6:461–464. doi: 10.1214/aos/1176344136
   Web of Science ®Google Scholar
• Mallows CL. Some Comments on Cjp. Technometrics. 1973;15(4):661–675.
   Web of Science ®Google Scholar
• Miller, A. Subset selection in regression. London: Chapman and Hall/CRC; 2002.
   Google Scholar
• Tibshirani R. Regression shrinkage and selection via LASSO. J R Stat Soc B. 1996;58:267–288.
   Google Scholar
• Efron B, Hastie T, Johnstone I, Tibshirani R. Least angle regression (with discussion). Ann Stat. 2004;32:409–499.
   Google Scholar
• Fan J, Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc. 2001;96:1348–1360. doi: 10.1198/016214501753382273
   Web of Science ®Google Scholar
• Zou H, Hastie T. Regularization and variable selection via the elastic net. J R Stat Soc B. 2005;67:301–320. doi: 10.1111/j.1467-9868.2005.00503.x
   Google Scholar
• Zou H. The adaptive lasso and its oracle properties. J Am Stat Assoc. 2006;101:1418–1429. doi: 10.1198/016214506000000735
   Web of Science ®Google Scholar
• Fan J, Lv J. Sure independence screening for ultrahigh dimensional feature space (with discussion). J R Stat Soc B. 2008;70:849–911. doi: 10.1111/j.1467-9868.2008.00674.x
   Google Scholar
• Li R, Zhong W, Zhu L. Feature screening via distance correlation learning. J Am Statist Assoc. 2012;107(499):1129–1139. doi: 10.1080/01621459.2012.695654
   PubMed Web of Science ®Google Scholar
• Fan J, Lv J. A selective overview of variable selection in high dimensional feature space. Statist Sin. 2010;20(1): 101–148.
   Google Scholar
• Liebetrau AM. Measures of association. London: Sage Publications; 2005.
   Google Scholar
• Gebelein, H. Das statistische problem der korrelation als variations - und eigenwerthproblem und sein zusammenhang mit der ausgleichsrechnung. Z Angew Math Mech. 1941;21:364–379. doi: 10.1002/zamm.19410210604
   Google Scholar
• Csáki P, Fischer J. On the general notion of maximum correlation. Magyar Tudományos Akad Mat Kutató Intézetenk Közleményei (publ. Math. Inst. Hungar Acad Sci). 1963;8:27–51.
   Google Scholar
• Koyak R. On measuring internal dependence in a set of random variables. Ann Stat. 1987;15:1215–1228.
   Google Scholar
• Sethuraman J. The asymptotic distribution of Rényi maximal correlation. Comm Stat Theory Methods. 1990;19:4291–4298. doi: 10.1080/03610929008830442
   Web of Science ®Google Scholar
• Dembo A, Kagan A, Shepp L. Remarks on the maximum correlation coefficient. Bernoulli. 2001;7:343–350.
   Google Scholar
• Novak, S. On Gebelein's correlation coefficient. Stat Probab Lett. 2004;69:299–303. doi: 10.1016/j.spl.2004.06.026
   Web of Science ®Google Scholar
• Yenigün CD, Székely GJ, Rizzo ML. A test of independence in two way contingency tables based on maximal correlation. Comm Stat: Theory Methods. 2011;40:2225–2242. doi: 10.1080/03610921003764274
   Web of Science ®Google Scholar
• Breiman L, Friedman J. Estimating optimal transformations for multiple regression and correlation (with discussion). J Amer Statist Assoc. 1985;80:580–619. doi: 10.1080/01621459.1985.10478157
   Web of Science ®Google Scholar
• Székely GJ, Rizzo ML, Bakirov NK. Measuring and testing dependence by correlation of distances. Ann Stat. 2007;35:2769–2794.
   Google Scholar
• Rizzo ML, Székely GJ. energy: E-statistics (energy statistics). R package version 1.5.0; 2013.
   Google Scholar
• R Development Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2013, ISBN 3-900051-07-0. Available from: http://www.R-project.org.
   Google Scholar
• Székely G, Rizzo ML. Brownian distance correlation. Ann Appl Stat. 2009;3(4):1236–1265.
   Google Scholar
• Székely GJ, Rizzo ML. On the uniqueness of distance covariance. Stat Probab Lett. 2012;82:2278–2282. doi: 10.1016/j.spl.2012.08.007
   Web of Science ®Google Scholar
• Dueck J, Edelmann D. Gneiting T, Richards D. The affinely invariant distance correlation. arXiv:1210.2482v1 [math.ST] 9 Oct 2012.
   Google Scholar
• Lyons R. Distance covariance in metric spaces. Ann Prob. 2013;41(5):3051–3696.
   Google Scholar
• Spector P, Friedman J, Tibshirani R, Lumley T. acepack: ACE and AVAS methods for choosing regression transformations. R package version 1.3-3.2; 2012.
   Google Scholar
• Mosteller F, Tukey JW. Data analysis and regression: a second course in statistics. Reading, MA: Addison-Wesley; 1977.
   Google Scholar