Statistics and Its Interface

Volume 2 (2009)

Number 4

A minimum discrepancy approach to multivariate dimension reduction via $k$-means inverse regression

Pages: 503 – 511

DOI: http://dx.doi.org/10.4310/SII.2009.v2.n4.a11

Authors

Akim Adekpedjou (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Mo., U.S.A.)

C. Messan Setodji (The Rand Corporation, Pittsburgh, Penn., U.S.A.)

Xuerong Meggie Wen (Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Mo., U.S.A.)

Abstract

We proposed a new method to estimate the intra-cluster adjusted central subspace for regressions with multivariate responses. Following Setodji and Cook (2004), we made use of the $k$-means algorithm to cluster the observed response vectors. Our method was designed to recover the intracluster information and outperformed previous method with respect to estimation accuracies on both the central subspace and its dimension. It also allowed us to test the predictor effects in a model-free approach. Simulation and a real data example were given to illustrate our methodology.

Keywords

multivariate regression, dimension reduction, central subspaces, intra-cluster information, k-means clustering

2010 Mathematics Subject Classification

Primary 62G08, 62H12. Secondary 62H30.

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