Department of Mathematics
A Sparse eigen-decomposition estimation for semiparametric models
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. © 2009 Elsevier B.V. All rights reserved.
Source Publication Title
Computational Statistics and Data Analysis
Zhu, Li-Ping, Zhou Yu, and Li-Xing Zhu. "A Sparse eigen-decomposition estimation for semiparametric models." Computational Statistics and Data Analysis 54.4 (2010): 976-986.