A sparse eigen-decomposition estimation in semiparametric regression

Li-Ping Zhu, Zhou Yu and Li-Xing Zhu

Computational Statistics & Data Analysis, 2010, vol. 54, issue 4, 976-986

Abstract: For semiparametric models, one of the key issues is to reduce the predictors' dimension so that the regression functions can be efficiently estimated based on the low-dimensional projections of the original predictors. Many sufficient dimension reduction methods seek such principal projections by conducting the eigen-decomposition technique on some method-specific candidate matrices. In this paper, we propose a sparse eigen-decomposition strategy by shrinking small sample eigenvalues to zero. Different from existing methods, the new method can simultaneously estimate basis directions and structural dimension of the central (mean) subspace in a data-driven manner. The oracle property of our estimation procedure is also established. Comprehensive simulations and a real data application are reported to illustrate the efficacy of the new proposed method.

Date: 2010
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