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Bayesian sieve method for piece-wise smooth regression

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  • Yi, Taihe
  • Wang, Zhengming

Abstract

We study the piece-wise smooth regression from a theoretical Bayesian perspective. Our results indicate that under some mild assumptions, the posterior of the regression model and the change-points locations contracts at optimal nonparametric convergence rate up to a log-factor, and the number of change-points is posterior consistent.

Suggested Citation

  • Yi, Taihe & Wang, Zhengming, 2017. "Bayesian sieve method for piece-wise smooth regression," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 5-11.
    • Handle: RePEc:eee:stapro:v:130:y:2017:i:c:p:5-11
    DOI: 10.1016/j.spl.2017.07.005
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    References listed on IDEAS

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    1. Weining Shen & Subhashis Ghosal, 2015. "Adaptive Bayesian Procedures Using Random Series Priors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1194-1213, December.
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    4. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve Prior," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 549-570, September.
    5. Jeng, X. Jessie & Cai, T. Tony & Li, Hongzhe, 2010. "Optimal Sparse Segment Identification With Application in Copy Number Variation Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1156-1166.
    6. Julyan Arbel & Ghislaine Gayraud & Judith Rousseau, 2013. "Bayesian Optimal Adaptive Estimation Using a Sieve prior," Working Papers 2013-19, Center for Research in Economics and Statistics.
    7. Gilles Teyssière & Alan P. Kirman (ed.), 2007. "Long Memory in Economics," Springer Books, Springer, number 978-3-540-34625-8, September.
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