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Activity Number:
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251
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Type:
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Contributed
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Date/Time:
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Tuesday, July 31, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Computing
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| Abstract - #308294 |
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Title:
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Asymptotic Mean Squared Prediction Error of L2Boosting Estimator Under Mis-specified Models
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Author(s):
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Tzu-Chang Cheng*+ and Ching-Kang Ing
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Companies:
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University of Illinois at Urbana-Champaign and Academia Sinica
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Address:
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Department of Economics, No 1306 North Lincoln Avenue, Urbana, IL, 61801,
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Keywords:
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Asymptotic Mean Squared Prediction Error ; L2Boosting ; Weak greedy algorithm ; Weak greedy orthogonal algorithm
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Abstract:
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A rigorous analysis of the L2Boosting predictor is given in a high-dimensional linear regression model, in which the number of regressors is much larger than the number of observations. Instead of boosting the predictor using the weak greedy algorithm (WGA) in Buhlmann (2006), this paper focuses on the weak orthogonal greedy algorithm (WOGA) because its statistical properties are more traceable. We explore the variable sequences determined by WOGA, and thereby give an asymptotic expression for the mean-squared prediction error (MSPE) of the corresponding Boosting predictor. This expression shows an algebraic tradeoff between the bias and variance terms. Finally, our simulation results suggest that the Boosting predictor based on WOGA outperforms the one based on WGA in terms of MSPE, offering an interesting direction for future research.
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