On hybrid methods of inverse regression-based algorithms

Authors:
Li-Xing Zhu;Megu Ohtaki;Yingxing Li
Affiliations:
Hong Kong Baptist University, Hong Kong, China and Renmin University of China, Beijing, China;Research Institute of Radiation Biology, Hiroshima, Japan;Cornell University, New York, USA
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

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.