Open Access
2011 Iterative application of dimension reduction methods
Amanda J. Shaker, Luke A. Prendergast
Electron. J. Statist. 5: 1471-1494 (2011). DOI: 10.1214/11-EJS650


The goal of this article is to introduce an iterative application of dimension reduction methods. It is known that in some situations, methods such as Sliced Inverse Regression (SIR), Ordinary Least Squares (OLS) and Cumulative Mean Estimation (CUME) are able to find only a partial basis for the dimension reduction subspace. However, for many models these methods are very good estimators of this partial basis. In this paper we propose a simple iterative procedure which differs from existing combined approaches in the sense that the initial partial basis is estimated first and the second dimension reduction approach seeks only the remainder of the dimension reduction subspace. Our approach is compared against that of existing combined dimension reduction approaches via simulated data as well as two example data sets.


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Amanda J. Shaker. Luke A. Prendergast. "Iterative application of dimension reduction methods." Electron. J. Statist. 5 1471 - 1494, 2011.


Published: 2011
First available in Project Euclid: 23 November 2011

zbMATH: 1271.62143
MathSciNet: MR2861694
Digital Object Identifier: 10.1214/11-EJS650

Primary: 62J02
Secondary: 62H30

Keywords: cumulative directional regression , cumulative mean estimation , cumulative variance estimation , Dimension reduction , ordinary least squares , principal hessian directions , sliced average variance estimation , sliced inverse regression

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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