Asymptotics for pooled marginal slicing estimator based on SIR[alpha] approach

Jérôme Saracco

Journal of Multivariate Analysis, 2005, vol. 96, issue 1, 117-135

Abstract: 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.

Keywords: Asymptotics; Dimension; reduction; subspaces; Eigen-elements; Pooled; marginal; slicing; Semiparametric; regression; model; Sliced; inverse; regression (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (6)

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