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Bayesian adaptive Lasso

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  • Chenlei Leng
  • Minh-Ngoc Tran
  • David Nott

Abstract

We propose the Bayesian adaptive Lasso (BaLasso) for variable selection and coefficient estimation in linear regression. The BaLasso is adaptive to the signal level by adopting different shrinkage for different coefficients. Furthermore, we provide a model selection machinery for the BaLasso by assessing the posterior conditional mode estimates, motivated by the hierarchical Bayesian interpretation of the Lasso. Our formulation also permits prediction using a model averaging strategy. We discuss other variants of this new approach and provide a unified framework for variable selection using flexible penalties. Empirical evidence of the attractiveness of the method is demonstrated via extensive simulation studies and data analysis. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Chenlei Leng & Minh-Ngoc Tran & David Nott, 2014. "Bayesian adaptive Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 221-244, April.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:2:p:221-244
    DOI: 10.1007/s10463-013-0429-6
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    References listed on IDEAS

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    1. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    2. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    3. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    4. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    5. Yuan, Ming & Lin, Yi, 2005. "Efficient Empirical Bayes Variable Selection and Estimation in Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1215-1225, December.
    6. Wang, Hansheng & Leng, Chenlei, 2007. "Unified LASSO Estimation by Least Squares Approximation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1039-1048, September.
    7. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

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    3. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
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    5. Sandra Stankiewicz, 2015. "Forecasting Euro Area Macroeconomic Variables with Bayesian Adaptive Elastic Net," Working Paper Series of the Department of Economics, University of Konstanz 2015-12, Department of Economics, University of Konstanz.
    6. Gallant, A. Ronald & Hong, Han & Leung, Michael P. & Li, Jessie, 2022. "Constrained estimation using penalization and MCMC," Journal of Econometrics, Elsevier, vol. 228(1), pages 85-106.
    7. Mallick, Himel & Yi, Nengjun, 2017. "Bayesian group bridge for bi-level variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 115-133.
    8. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    9. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    10. Sakae Oya, 2021. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Papers 2103.05880, arXiv.org, revised Mar 2022.
    11. Canhong Wen & Xueqin Wang & Shaoli Wang, 2015. "Laplace Error Penalty-based Variable Selection in High Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 685-700, September.
    12. Feng, Xiangnan & Lu, Bin & Song, Xinyuan & Ma, Shuang, 2019. "Financial literacy and household finances: A Bayesian two-part latent variable modeling approach," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 119-137.
    13. Zhao, Weihua & Lian, Heng & Zhang, Riquan & Lai, Peng, 2016. "Estimation and variable selection for proportional response data with partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 40-56.
    14. Feng, Xiang-Nan & Wang, Yifan & Lu, Bin & Song, Xin-Yuan, 2017. "Bayesian regularized quantile structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 234-248.
    15. Chowdhury, K.P., 2023. "Nonparametric functional analysis under joint estimation with applications to identifying highly cited papers," Journal of Informetrics, Elsevier, vol. 17(4).
    16. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2022. "Variational inference for large Bayesian vector autoregressions," Papers 2202.12644, arXiv.org, revised Jun 2023.
    17. Na Shan & Ping-Feng Xu, 2024. "Bayesian Adaptive Lasso for Detecting Item–Trait Relationship and Differential Item Functioning in Multidimensional Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 89(4), pages 1337-1365, December.
    18. Sakae Oya, 2022. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(3), pages 507-526, September.

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