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Bayesian boundary trend filtering

Author

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  • Onizuka, Takahiro
  • Iwashige, Fumiya
  • Hashimoto, Shintaro

Abstract

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

Suggested Citation

  • Onizuka, Takahiro & Iwashige, Fumiya & Hashimoto, Shintaro, 2024. "Bayesian boundary trend filtering," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:csdana:v:191:y:2024:i:c:s0167947323002001
    DOI: 10.1016/j.csda.2023.107889
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    References listed on IDEAS

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    1. Daouia, Abdelaati & Simar, Léopold, 2005. "Robust nonparametric estimators of monotone boundaries," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 311-331, October.
    2. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    3. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2021. "Robustified Expected Maximum Production Frontiers," Econometric Theory, Cambridge University Press, vol. 37(2), pages 346-387, April.
    4. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    5. Leonie Selk & Charles Tillier & Orlando Marigliano, 2022. "Multivariate boundary regression models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 400-426, March.
    6. Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
    7. Abdelaati Daouia & Hohsuk Noh & Byeong U. Park, 2016. "Data envelope fitting with constrained polynomial splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 3-30, January.
    8. N. G. Polson & J. G. Scott, 2013. "Data augmentation for non-Gaussian regression models using variance-mean mixtures," Biometrika, Biometrika Trust, vol. 100(2), pages 459-471.
    9. Daouia, Abdelaati & Laurent, Thibault & Noh, Hohsuk, 2017. "npbr: A Package for Nonparametric Boundary Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i09).
    10. Patricio Aceituno & Maríadel Prieto & María Solari & Alejandra Martínez & Germán Poveda & Mark Falvey, 2009. "The 1877–1878 El Niño episode: associated impacts in South America," Climatic Change, Springer, vol. 92(3), pages 389-416, February.
    11. Hall, Peter & Park, Byeong U. & Stern, Steven E., 1998. "On Polynomial Estimators of Frontiers and Boundaries," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 71-98, July.
    12. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    13. Nicholas Syring & Ryan Martin, 2019. "Calibrating general posterior credible regions," Biometrika, Biometrika Trust, vol. 106(2), pages 479-486.
    14. Daouia, Abdelaati & Noh, Hohsuk & Park, Byeong U., 2016. "Data envelope fitting with constrained polynomial splines," LIDAM Reprints ISBA 2016011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    16. Reiß, Markus & Schmidt-Hieber, Johannes, 2020. "Posterior contraction rates for support boundary recovery," Stochastic Processes and their Applications, Elsevier, vol. 130(11), pages 6638-6656.
    17. Oscar Hernan Madrid Padilla & Sabyasachi Chatterjee, 2022. "Risk bounds for quantile trend filtering [-penalized quantile regression in high-dimensional sparse models]," Biometrika, Biometrika Trust, vol. 109(3), pages 751-768.
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