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Regression with stagewise minimization on risk function

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  • Yoshida, Takuma
  • Naito, Kanta

Abstract

This paper studies a curve estimation based on empirical risk minimization. The estimator is composed as a convex combination of words (learners) in a dictionary. A word is selected in each step of the proposed stagewise algorithm, which minimizes a certain divergence measure. A non-asymptotic error bound of the estimator is developed, and it is shown that the error bound becomes sharp as the number of iterations of the algorithm increases. A simulation study and real data example confirm the performance of the estimator.

Suggested Citation

  • Yoshida, Takuma & Naito, Kanta, 2019. "Regression with stagewise minimization on risk function," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 123-143.
    • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:123-143
    DOI: 10.1016/j.csda.2018.12.011
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    References listed on IDEAS

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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    3. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    4. Chunming Zhang & Yuan Jiang & Yi Chai, 2010. "Penalized Bregman divergence for large-dimensional regression and classification," Biometrika, Biometrika Trust, vol. 97(3), pages 551-566.
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