Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-21T16:31:21.475Z Has data issue: false hasContentIssue false
  • English
  • Français

An Introduction to Dimension Reduction in Nonparametric KernelRegression

Published online by Cambridge University Press:  23 January 2015

S. Girard  and
J. Saracco
S. Girard
Affiliation:
Inria Grenoble Rhône-Alpes & Laboratoire Jean Kuntzmann, France
J. Saracco
Affiliation:
Institut Polytechnique de Bordeaux & Inria Bordeaux Sud Ouest & Institut de Mathématiques de Bordeaux, France
Get access

Abstract

Nonparametric regression is a powerful tool to estimate nonlinear relations between some predictors and a response variable. However, when the number of predictors is high, nonparametric estimators may suffer from the curse of dimensionality. In this chapter, we show how a dimension reduction method (namely Sliced Inverse Regression) can be combined with nonparametric kernel regression to overcome this drawback. The methods are illustrated both on simulated datasets as well as on an astronomy dataset using the R software.

Type
Research Article
Information
European Astronomical Society Publications Series , Volume 66: Statistics for Astrophysics Methods and Applications of the Regression , 2014 , pp. 167 - 196
Copyright
© EAS, EDP Sciences, 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aragon, Y., & Saracco, , 1997, J., Comput. Stat., 12, 109
Azaïs, R., Gégout-Petit, A., & Saracco, J., 2012, J. Stat. Plann. Infer. 142, 481CrossRef
Bai, Z.D., & He, X., 2004, J. Multivariate Anal., 88, 109CrossRef
Barreda, L., Gannoun, A., & Saracco, J., 2007, J. Stat. Comp. Simul., 77, 1CrossRef
Bercu, B., Nguyen, T.M.N., & Saracco, J., 2011, J. Korean Stat. Soc., 41, 17CrossRef
Bernard-Michel, C., Douté, S., Fauvel, M., Gardes, L., & Girard, S., 2009a, J. Geophys. Res. – Planets, 114
Bernard-Michel, C., Gardes, L., & Girard, S., 2009b, Stat. Comput., 19, 85CrossRef
Bura, E., & Cook, R.D., 2001, J. Roy. Statis. Soc. Ser. B. Stat. Meth., 63, 393CrossRef
Carroll, R.J., & Li, K.-C., 1992, J. Am. Stat. Assoc., 87, 1040CrossRef
Chen, C.-H., & Li, K.-C., 1998, Stat. Sinica, 8, 289
Cook, R.D., 2000, Comm. Stat. – Theory Meth., 29, 2109CrossRef
Cook, R.D., 1998, J. Am. Stat. Assoc., 93, 84CrossRef
Coudret, R., Girard, S., & Saracco, J., 2013, [http://hal.inria.fr/hal00714981]
Coudret, R., Liquet, B., & Saracco, J., 2014, J. Soc. Française Stat. (in press)
Duan, N., & Li, K.-C., 1991, Ann. Stat., 19, 505CrossRef
Ferraty, F., & Vieu, P., 2006 (Springer)
Ferré, L., 1998, J. Am. Stat. Assoc., 93, 132
Hall, P., & Li, K.-C., 1993, Ann. Stat., 21, 867CrossRef
Härdle, W., 1990 (Cambridge University Press)
Hastie, T., Tibshirani, R., & Friedman, J., 2009, Springer Series in Statistics (Springer)Google Scholar
Hsing, T., 1999, Ann. Stat., 27, 697CrossRef
Hsing, T., & Carroll, R.J., 1992, Ann. Stat., 20, 1040CrossRef
Kuentz, V., Liquet, B., & Saracco, J., 2010, Comm. Stat., Theory Meth. 39, 1985CrossRef
Li, K.-C., 1991, J. Am. Stat. Assoc., 86, 316CrossRef
Li, K.-C., Aragon, Y., Shedden, K., & Agnan, C.T., 2003, J. Am. Stat. Assoc., 98, 99CrossRef
Li, L., & Yin, X., 2008, Biometrics, 64, 124CrossRef
Li, Y., & Zhu, L., 2007, Ann. Stat., 35, 41CrossRef
Liquet, B., & Saracco, J., 2012, Comput. Stat., 27, 103CrossRef
Liquet, B., & Saracco, J., 2008, Comm. Stat., Simul. Comput., 37, 1198CrossRef
Lue, H.-H., 2009, J. Stat. Plann. Infer., 139, 2656CrossRef
Moler, C.B., & Stewart, G.W., 1973, SIAM J. Numer. Anal., 10, 241CrossRef
Nadaraya, E.A., 1964, Theory Prob. Appl. 9, 141CrossRef
Parzen, E., 1962, Ann. Math. Stat., 33, 1065CrossRef
Prendergast, L.A., 2007, Biometrika, 94, 585CrossRef
Rosenblatt, M., 1956, Ann. Math. Stat., 832CrossRef
Saracco, J., 2005, J. Mult. Anal., 96, 117CrossRef
Saracco, J., 2001, Commu. Stat., Simul. Comput., 30, 489CrossRef
Saracco, J., 1997, Commun. Stat. Theory Meth., 26, 2141CrossRef
Schott, J.R., 1994, J. Am. Stat. Assoc., 89, 141CrossRef
Schimek, M., 2000 (Wiley)
Scrucca, L., 2007, Comput. Stat. Data Anal., 52, 438CrossRef
Setodji, C.M., & Cook, R.D., 2004, Technometrics, 46, 421CrossRef
Shao, Y., Cook, R.D., & Weisberg, S., 2009, J. Stat. Plann. Infer., 139, 952CrossRef
Yin, X., & Seymour, L., 2007, Stat. Sinica, 15, 1069
Watson, G.S., 1964, Smooth Regression Analysis. Sankhya: The Indian J. Stat. Ser. A, 26, 359
Zhong, W., Zeng, P., Ma, P., Liu, J.S., & Zhu, Y., 2005, Bioinformatics, 21, 4169CrossRef
Zhu, L.X., & Fang, K.T., 1996, Ann. Stat., 24, 1053
Zhu, L.X., & Ng, K.W., 1995, Stat. Sinica, 5, 727
Zhu, L.X., Ohtaki, M., & Li, Y., 2007, Comput. Stat., 51, 2621
Zhu, L., & Zhu, L., 2007, J. Multivariate Anal., 98, 970CrossRef