Minimax adaptive dimension reduction for regression

@article{Paris2014MinimaxAD,
  title={Minimax adaptive dimension reduction for regression},
  author={Quentin Paris},
  journal={J. Multivariate Analysis},
  year={2014},
  volume={128},
  pages={186-202}
}
In this paper, we address the problem of regression estimation in the context of a p-dimensional predictor when p is large. We propose a general model in which the regression function is a composite function. Our model consists in a nonlinear extension of the usual sufficient dimension reduction setting. The strategy followed for estimating the regression function is based on the estimation of a new parameter, called the reduced dimension. We adopt a minimax point of view and provide both lower… CONTINUE READING

Citations

Publications citing this paper.

Supplement to : Minimax adaptive dimension reduction for regression

Quentin, IRMAR, ENS Cachan Bretagne
2013
View 3 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-10 of 26 references

A Distribution-Free Theory of Nonparametric Regression

Springer series in statistics • 2002
View 6 Excerpts
Highly Influenced

Sliced Inverse Regression for Dimension Reduction

LI KER-CHAU
2010
View 4 Excerpts
Highly Influenced

Investigating smooth multiple regression by the method of average derivative

W. Härdle, T. M. Stoker
Journal of the American Statistical Association, • 1989
View 4 Excerpts
Highly Influenced

Constructive Approximation: Advanced Problems

G. G. Lorentz, M.v. Golitschek, Y. Makovoz
1996
View 2 Excerpts
Highly Influenced

Introduction to Nonparametric Estimation

Springer series in statistics • 2009
View 2 Excerpts

Similar Papers

Loading similar papers…