The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Generalized Thresholding of Large Covariance Matrices
Abstract
We propose a new class of generalized thresholding operators that combine thresholding with shrinkage, and study generalized thresholding of the sample covariance matrix in high dimensions. Generalized thresholding of the covariance matrix has good theoretical properties and carries almost no computational burden. We obtain an explicit convergence rate in the operator norm that shows the tradeoff between the sparsity of the true model, dimension, and the sample size, and shows that generalized thresholding is consistent over a large class of models as long as the dimension p and the sample size n satisfy log p/n → 0. In addition, we show that generalized thresholding has the “sparsistency” property, meaning it estimates true zeros as zeros with probability tending to 1, and, under an additional mild condition, is sign consistent for nonzero elements. We show that generalized thresholding covers, as special cases, hard and soft thresholding, smoothly clipped absolute deviation, and adaptive lasso, and compare different types of generalized thresholding in a simulation study and in an example of gene clustering from a microarray experiment with tumor tissues.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
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
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Cluster analysis and display of genome-wide expression patterns
Eisen, M. B., Spellman, P. T., Brown, P. O., & Botstein, D. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.25.14863 · Cited by 16,184
Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties
Fan, J., & Li, R. (2001) · Journal of the American Statistical Association · doi:10.1198/016214501753382273 · Cited by 8,900
Ideal spatial adaptation by wavelet shrinkage
Donoho, D. L., & Johnstone, I. M. (1994) · Biometrika · doi:10.1093/biomet/81.3.425 · Cited by 8,760
The adaptive lasso and its oracle properties
Zou, H. (2006) · Journal of the American Statistical Association · doi:10.1198/016214506000000735 · Cited by 7,470
Sparse inverse covariance estimation with the graphical lasso
Friedman, J., Hastie, T., & Tibshirani, R. (2008) · Biostatistics · doi:10.1093/biostatistics/kxm045 · Cited by 6,355
Khan, J., Wei, J. S., Ringnér, M., Saal, L. H., Ladanyi, M., Westermann, F., Berthold, F., Schwab, M., Antonescu, C. R., Peterson, C., et al. (2001) · Nature Medicine · doi:10.1038/89044 · Cited by 2,644
On the distribution of the largest eigenvalue in principal components analysis
Johnstone, I. M. (2001) · The Annals of Statistics · doi:10.1214/aos/1009210544 · Cited by 1,949
Wavelet Shrinkage: Asymptopia?
Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., & Picard, D. (1995) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1995.tb02032.x · Cited by 1,749
Cited by
Large Covariance Estimation by Thresholding Principal Orthogonal Complements
Fan, J., Liao, Y., & Mincheva, M. (2013) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12016 · Cited by 909
Sparse estimation of a covariance matrix
Bien, J., & Tibshirani, R. J. (2011) · Biometrika · doi:10.1093/biomet/asr054 · Cited by 342
Robust and sparse correlation matrix estimation for the analysis of high-dimensional genomics data
Serra, A., Coretto, P., Fratello, M., & Tagliaferri, R. (2018) · Bioinformatics · doi:10.1093/bioinformatics/btx642 · Cited by 25
Metadata
- Authors
- Rothman, A. J., Levina, E., & Zhu, J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2009-03
- Volume
- 104
- Issue
- 485
- Pages
- 177-186
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2057535756
- Cited by
- 489
- References
- 33
- FWCI
- 15.58
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Generalized Thresholding of Large Covariance Matrices. https://app.cochat.ai/papers/10.1198/jasa.2009.0101
- The paper
- Rothman, A. J., Levina, E., & Zhu, J. (2009). Generalized Thresholding of Large Covariance Matrices. Journal of the American Statistical Association. https://doi.org/10.1198/jasa.2009.0101
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
