Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 101, Issue 474, Pages 630-643Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214505000001285
Keywords
central dimension-reduction subspace; convergence rate; dimensionality determination; sliced inverse regression
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Sliced inverse regression is a promising method for the estimation of the central dimension-reduction subspace (CDR space) in semiparametric regression models. It is particularly useful in tackling cases with high-dimensional covariates. In this article we study the asymptotic behavior of the estimate of the CDR space with high-dimensional covariates, that is, when the dimension of the covariates goes to infinity as the sample size goes to infinity. Strong and weak convergence are obtained. We also suggest an estimation procedure of the Bayes information criterion type to ascertain the dimension of the CDR space and derive the consistency. A simulation study is conducted.
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