The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
Bayesian linear regression with sparse priors
Open accessAbstract
We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the posterior distribution is shown to contract at the optimal rate for recovery of the unknown sparse vector, and to give optimal prediction of the response vector. It is also shown to select the correct sparse model, or at least the coefficients that are significantly different from zero. The asymptotic shape of the posterior distribution is characterized and employed to the construction and study of credible sets for uncertainty quantification.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Nearly unbiased variable selection under minimax concave penalty
Zhang, C.-H. (2010) · The Annals of Statistics · doi:10.1214/09-aos729 · Cited by 3,835
Simultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., & Tsybakov, A. B. (2009) · The Annals of Statistics · doi:10.1214/08-aos620 · Cited by 2,396
Stable recovery of sparse overcomplete representations in the presence of noise
Donoho, D. L., Elad, M., & Temlyakov, V. N. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.860430 · Cited by 2,183
The Dantzig selector: Statistical estimation when p is much larger than n
Candes, E., & Tao, T. (2007) · The Annals of Statistics · doi:10.1214/009053606000001523 · Cited by 1,747
Bayesian Variable Selection in Linear Regression
Mitchell, T. J., & Beauchamp, J. J. (1988) · Journal of the American Statistical Association · doi:10.1080/01621459.1988.10478694 · Cited by 1,424
The horseshoe estimator for sparse signals
Carvalho, C. M., Polson, N. G., & Scott, J. G. (2010) · Biometrika · doi:10.1093/biomet/asq017 · Cited by 1,381
Spike and slab variable selection: Frequentist and Bayesian strategies
Ishwaran, H., & Rao, J. S. (2005) · The Annals of Statistics · doi:10.1214/009053604000001147 · Cited by 1,033
On the conditions used to prove oracle results for the Lasso
van de Geer, S. A., & Bühlmann, P. (2009) · Electronic Journal of Statistics · doi:10.1214/09-ejs506 · Cited by 684
Convergence rates of posterior distributions
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A simple new approach to variable selection in regression, with application to genetic fine mapping
Wang, G., Sarkar, A., Carbonetto, P., & Stephens, M. (2020) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12388 · Cited by 1,121
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
Simpson, D., Rue, H., Riebler, A., Martins, T. G., & Sørbye, S. H. (2017) · Statistical Science · doi:10.1214/16-sts576 · Cited by 1,085
Model Averaging and Its Use in Economics
Steel, M. F. J. (2020) · Journal of Economic Literature · doi:10.1257/jel.20191385 · Cited by 321
Metadata
- Authors
- Castillo, I., Schmidt-Hieber, J., & van der Vaart, A.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2015-10-01
- Volume
- 43
- Issue
- 5
- Pages
- 1986-2018
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1711911837
- Cited by
- 277
- References
- 39
- FWCI
- 11.10
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
