Abstract
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.
Original language | English |
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Pages (from-to) | 630-643 |
Number of pages | 14 |
Journal | Journal of the American Statistical Association |
Volume | 101 |
Issue number | 474 |
DOIs | |
Publication status | Published - Jun 2006 |
Scopus Subject Areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
User-Defined Keywords
- Central dimension-reduction subspaee
- Convergence rate
- Dimensionality determination
- Sliced inverse regression