Robust minimax Stein estimation under invariant data-based loss for spherically and elliptically symmetric distributions
Author
Abstract
Suggested Citation
DOI: 10.1007/s00184-014-0512-x
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Fourdrinier, Dominique & Strawderman, William E., 1996. "A Paradox Concerning Shrinkage Estimators: Should a Known Scale Parameter Be Replaced by an Estimated Value in the Shrinkage Factor?," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 109-140, November.
- Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
- Cellier, D. & Fourdrinier, D., 1995. "Shrinkage Estimators under Spherical Symmetry for the General Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 338-351, February.
- Fourdrinier, Dominique & Strawderman, William, 2014. "On the non existence of unbiased estimators of risk for spherically symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 6-13.
- Fourdrinier, D. & Wells, M. T., 1995. "Loss Estimation for Spherically Symmetrical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 311-331, May.
- Cellier, Dominique & Fourdrinier, Dominique & Robert, Christian, 1989. "Robust shrinkage estimators of the location parameter for elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 39-52, April.
- T. Kubokawa & C. Robert & A. Saleh, 1991. "Robust estimation of common regression coefficients under spherical symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 677-688, December.
- Dominique Fourdrinier & William Strawderman & Martin Wells, 2006. "Estimation of a Location Parameter with Restrictions or “vague information” for Spherically Symmetric Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 73-92, March.
- Fourdrinier, Dominique & Strawderman, William E. & Wells, Martin T., 2003. "Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 24-39, April.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Ruili Sun & Tiefeng Ma & Shuangzhe Liu, 2018. "A Stein-type shrinkage estimator of the covariance matrix for portfolio selections," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 931-952, November.
- Fourdrinier, Dominique & Haddouche, Anis M. & Mezoued, Fatiha, 2021. "Covariance matrix estimation under data-based loss," Statistics & Probability Letters, Elsevier, vol. 177(C).
- Stéphane Canu & Dominique Fourdrinier, 2023. "Data based loss estimation of the mean of a spherical distribution with a residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 851-878, November.
- Hamid Karamikabir & Nasrin Karamikabir & Mohammad Ali Khajeian & Mahmoud Afshari, 2023. "Bayesian Wavelet Stein’s Unbiased Risk Estimation of Multivariate Normal Distribution Under Reflected Normal Loss," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-20, March.
- Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Kubokawa, T. & Srivastava, M. S., 2001. "Robust Improvement in Estimation of a Mean Matrix in an Elliptically Contoured Distribution," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 138-152, January.
- Aurélie Boisbunon & Stéphane Canu & Dominique Fourdrinier & William Strawderman & Martin T. Wells, 2014. "Akaike's Information Criterion, C p and Estimators of Loss for Elliptically Symmetric Distributions," International Statistical Review, International Statistical Institute, vol. 82(3), pages 422-439, December.
- Fourdrinier Dominique & Strawderman William E. & Wells Martin T., 2009. "Improved estimation for elliptically symmetric distributions with unknown block diagonal covariance matrix," Statistics & Risk Modeling, De Gruyter, vol. 26(3), pages 203-217, April.
- Fourdrinier, Dominique & Strawderman, William E. & Wells, Martin T., 2003. "Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 24-39, April.
- Fourdrinier, Dominique & Strawderman, William, 2014. "On the non existence of unbiased estimators of risk for spherically symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 6-13.
- Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
- Jurečková Jana & Sen P. K., 2006. "Robust multivariate location estimation, admissibility, and shrinkage phenomenon," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 273-290, December.
- Fourdrinier, Dominique & Mezoued, Fatiha & Wells, Martin T., 2016. "Estimation of the inverse scatter matrix of an elliptically symmetric distribution," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 32-55.
- Evgeny Pchelintsev, 2013. "Improved estimation in a non-Gaussian parametric regression," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 15-28, April.
- Ouassou, Idir & Strawderman, William E., 2002. "Estimation of a parameter vector restricted to a cone," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 121-129, January.
- Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
- Dominique Fourdrinier & Othmane Kortbi & William Strawderman, 2014. "Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions with residual vector," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(2), pages 285-296, February.
- K. Krishnamoorthy, 1991. "Estimation of a common multivariate normal mean vector," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 761-771, December.
- Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
- Fourdrinier, Dominique & Strawderman, William E., 2016. "Stokes’ theorem, Stein’s identity and completeness," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 224-231.
- Chang, Ching-Hui & Pal, Nabendu, 2008. "Testing on the common mean of several normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 321-333, December.
- Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
- Tsai, Ming-Tien & Kubokawa, Tatsuya, 2007. "Estimation of Wishart mean matrices under simple tree ordering," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 945-959, May.
- E. A. Pchelintsev & S. M. Pergamenshchikov, 2018. "Oracle inequalities for the stochastic differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 469-483, July.
- William E. Strawderman & Andrew L. Rukhin, 2010. "Simultaneous estimation and reduction of nonconformity in interlaboratory studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 219-234, March.
More about this item
Keywords
Stein type identity; Stein–Haff type identity; Location parameter; Spherically symmetric distributions; Elliptically symmetric distributions; Minimaxity; Data-based losses;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:78:y:2015:i:4:p:461-484. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.