Application of the bootstrap approach to the choice of dimension and the a parameter in the SIRa method.

Liquet, Benoit and Saracco, Jerome (2008) Application of the bootstrap approach to the choice of dimension and the a parameter in the SIRa method.. Communication in Statistics - Simulation and computation, 37 6: 1198-1218. doi:10.1080/03610910801889011


Author Liquet, Benoit
Saracco, Jerome
Title Application of the bootstrap approach to the choice of dimension and the a parameter in the SIRa method.
Formatted title
Application of the bootstrap approach to the choice of dimension and the α parameter in the SIRα method.
Journal name Communication in Statistics - Simulation and computation   Check publisher's open access policy
ISSN 0361-0918
1532-4141
Publication date 2008
Year available 2008
Sub-type Article (original research)
DOI 10.1080/03610910801889011
Volume 37
Issue 6
Start page 1198
End page 1218
Total pages 21
Place of publication Philadelphia, PA, United States
Publisher Taylor & Francis
Language eng
Formatted abstract
To reduce the dimensionality of regression problems, sliced inverse regression approaches make it possible to determine linear combinations of a set of explanatory variables X related to the response variable Y in general semiparametric regression context. From a practical point of view, the determination of a suitable dimension (number of the linear combination of X) is important. In the literature, statistical tests based on the nullity of some eigenvalues have been proposed. Another approach is to consider the quality of the estimation of the effective dimension reduction (EDR) space. The square trace correlation between the true EDR space and its estimate can be used as goodness of estimation. In this article, we focus on the SIRα method and propose a naïve bootstrap estimation of the square trace correlation criterion. Moreover, this criterion could also select the α parameter in the SIRα method. We indicate how it can be used in practice. A simulation study is performed to illustrate the behavior of this approach.
Keyword Bootstrap
Dimension reduction
Sliced inverse regression
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Published online 22 May 2008

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Tue, 17 Sep 2013, 12:39:43 EST by Kay Mackie on behalf of School of Mathematics & Physics