Advertisement

Combining Factor Models and Variable Selection in High-Dimensional Regression

Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

This presentation provides a summary of some of the results derived in Kneip and Sarda (2011). The basic motivation of the study is to combine the points of view of model selection and functional regression by using a factor approach. For highly correlated regressors the traditional assumption of a sparse vector of parameters is restrictive. We therefore propose to include principal components as additional explanatory variables in an augmented regression model.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bickel, P.J., Ritov, Y., Tsybakov, A.: Simulataneous analysis of Lasso and Dantzig selector. Ann. Stat., 37, 1705–1732 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Cai, T., Hall, P.: Prediction in functional linear regression. Ann. Stat. 34, 2159–2179 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cand`es, E., Tao, T.: The Dantzig selector: statistical estimation when p is much larger than n. Ann. Stat. 35, 2013–2351 (2007)Google Scholar
  4. 4.
    Cardot, H., Ferraty, F., Sarda, P.: Functional linear model. Stat. Probab. Lett. 45, 11–22 (1999)MathSciNetMATHGoogle Scholar
  5. 5.
    Cardot, H., Mas, A., Sarda, P.: CLT in functional linear regression models. Probab. Theor. Rel. 138, 325–361 (2007)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Crambes, C., Kneip, A., Sarda, P.: Smoothing spline estimators for functional linear regression. Ann. Stat. 37, 35–72 (2009)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Cuevas, A., Febrero, M., Fraiman, R.: Linear functional regression: the case of fixed design and functional response. Canad. J. Stat. 30, 285–300 (2002)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Hall, P., Horowitz, J.L.: Methodology and convergence rates for functional linear regression. Ann. Stat. 35, 70–91 (2007)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Kneip, A., Sarda, P.: Factor Models and Variable Selection in High Dimensional Regression Analysis. Revised manuscript (2011)Google Scholar
  10. 10.
    Meinshausen, N., Bühlmann, P.: High dimensional graphs and variable selection with the Lasso. Ann. Stat. 34, 1436–1462 (2006)MATHCrossRefGoogle Scholar
  11. 11.
    Ramsay, J.O., Dalzell, C.J.: Some tools for functional data analysis (with discussion). J. Roy. Stat. Soc. B 53, 539–572 (1991)MathSciNetMATHGoogle Scholar
  12. 12.
    Tibshirani, R.: Regression shrinkage and selection via the Lasso. J. Roy. Stat. Soc. B 58, 267–288 (1996)MathSciNetMATHGoogle Scholar
  13. 13.
    van de Geer, S.: High-dimensional generalized linear models and the Lasso. Ann. Stat. 36, 614–645 (2008)MATHCrossRefGoogle Scholar
  14. 14.
    Yao, F., Müller, H.-G., Wang, J.-L.: Functional regression analysis for longitudinal data. Ann. Stat. 37, 2873–2903 (2005)CrossRefGoogle Scholar
  15. 15.
    Zhao, P., Yu, B.: On model selection consistency of Lasso. J. Machine Learning Research 7, 2541–2567 (2006)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Universität BonnBonnGermany
  2. 2.Institut de Mathématiques de ToulouseToulouseFrance

Personalised recommendations