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Activity Number: 466
Type: Contributed
Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #305278
Title: An Efficient Pathwise Variable Selection Criterion in Weakly Sparse Regression Models
Author(s): Ching-Kang Ing*+
Companies: Academia Sinica
Address: 128, Academia Rd. Sec. 2, Taipei 115 Taiwan, , Taiwan, Republic of China
Keywords: orthogonal greedy algorithm ; weak sparsity ; high-dimensional Akaike's information criterion ; asymptotically efficient rate

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with random regressors. A rate of convergence of the OGA predictor is obtained under the weak sparsity condition, which assumes that the ath powers, 0< a=1, of the absolute regression coefficients are summable. In addition, we introduce a method, called high-dimensional Akaike's information criterion (HDAIC), to determine the number of the OGA iterations, and show that OGA+HDAIC can achieve asymptotically efficient rate in situations where a is unknown.

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