Asymptotics for pooled marginal slicing estimator based on SIRα approach

By Jérôme Saracco. 2005

51 citations recorded by the source corpus.

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"@a 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.

Subfields: Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b7faec12ffc4f3f66377ec821dd3cc9f2257b478

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In Computational Theory and Mathematics

1. Song-qiao Wen
2. Bing Li
3. Lixing Zhu

In Statistics and Probability

1. Lixing Zhu
2. Song-qiao Wen
3. Bing Li
4. Xiangrong Yin
5. R. Dennis Cook
6. Liugen Xue
7. Yingcun Xia
8. Chenlei Leng

Citations in the corpus

• On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “|X or, equivalently, span[M(t)] ⊆ SY|X.”