Asymptotics for pooled marginal slicing estimator based on SIR[alpha] approach
Pooled marginal slicing (PMS) is a semiparametric method, based on sliced inverse regression (SIR) approach, for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we consider the SIR[alpha] version (combining the SIR-I and SIR-II approaches) of the PMS estimator and we establish the asymptotic distribution of the estimated matrix of interest. Then the asymptotic normality of the eigenprojector on the estimated effective dimension reduction (e.d.r.) space is derived as well as the asymptotic distributions of each estimated e.d.r. direction and its corresponding eigenvalue.
Year of publication: |
2005
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Authors: | Saracco, Jérôme |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 96.2005, 1, p. 117-135
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Publisher: |
Elsevier |
Keywords: | Asymptotics Dimension reduction subspaces Eigen-elements Pooled marginal slicing Semiparametric regression model Sliced inverse regression |
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