On hybrid methods of inverse regression-based algorithms

This paper is two-fold. First, we present a further investigation for the hybrid methods of inverse regression-based algorithms. This investigation provides the evidence of how the hybrids gain the advantages to become more powerful methods than the existing methods when the central dimension reduct...

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Bibliographic Details
Published in:Computational statistics & data analysis 2007-02, Vol.51 (5), p.2621-2635
Main Authors: Zhu, Li-Xing, Ohtaki, Megu, Li, Yingxing
Format: Article
Language:English
Subjects:
Dimension reduction
Exact sciences and technology
General topics
Hybrid methods
Linear inference, regression
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Sliced average variance estimation
Sliced inverse regression
Statistics
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Summary:This paper is two-fold. First, we present a further investigation for the hybrid methods of inverse regression-based algorithms. This investigation provides the evidence of how the hybrids gain the advantages to become more powerful methods than the existing methods when the central dimension reduction (CDR) space is estimated. Second, a Bayes Information Criterion (BIC)-type algorithm is recommended to estimate the dimension of the CDR space. Differing from the popularly used sequential test methods, the new algorithm does not require the asymptotic normality of the estimator of the inverse regression-based matrix. The BIC-based estimator is proven to be consistent. A set of simulations for several typical models were carried out to guide the selection of coefficient in the hybrids.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2006.01.005