Performance Limits for Estimators of the Risk or Distribution of Shrinkage-Type Estimators, and Some General Lower Risk-Bound Results
AbstractWe consider the problem of estimating measures of precision of shrinkage-type estimators like their risk or distribution. The notion of shrinkage-type estimators here refers to estimators like the James-Stein estimator or Lasso-type estimators, as well as to "thresholding" estimators such as, e. g., Hodges´so-called superefficient estimator. While the precision measures of such estimators typically can be estimated consistently, we show that they cannot be estimated uniformly consistently (even locally). This follows as a corollary to (locally) uniform lower bounds on the performance of estimators of the precision measures that we obtein in the paper. These lower bounds are typically quite large (e. g., they approach 1/2 or 1 depending on the situation considered). The analysis is based on some general lower risk bounds and related general results on the (non)existence of uniformly consistent estimators also obtained in the paper
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number 0301.
Date of creation: Jan 2003
Date of revision:
Contact details of provider:
Web page: http://www.univie.ac.at/vwl
Other versions of this item:
- Leeb, Hannes & P tscher, Benedikt M., 2006. "Performance Limits For Estimators Of The Risk Or Distribution Of Shrinkage-Type Estimators, And Some General Lower Risk-Bound Results," Econometric Theory, Cambridge University Press, vol. 22(01), pages 69-97, February.
- NEP-ALL-2003-01-19 (All new papers)
- NEP-CFN-2003-01-19 (Corporate Finance)
- NEP-ECM-2003-01-19 (Econometrics)
- NEP-RMG-2003-01-19 (Risk Management)
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Pötscher, Benedikt M., 2006. "The Distribution of Model Averaging Estimators and an Impossibility Result Regarding Its Estimation," MPRA Paper 73, University Library of Munich, Germany, revised Jul 2006.
- Leeb, Hannes & Potscher, Benedikt M., 2008.
"Sparse estimators and the oracle property, or the return of Hodges' estimator,"
Journal of Econometrics,
Elsevier, vol. 142(1), pages 201-211, January.
- Hannes Leeb & Benedikt M. Poetscher, 2005. "Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator," Cowles Foundation Discussion Papers 1500, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
- Pötscher, Benedikt M. & Leeb, Hannes, 2007.
"On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding,"
5615, University Library of Munich, Germany.
- Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
- Christian T. Brownlees & Giampiero Gallo, 2008.
"Comparison of Volatility Measures: a Risk Management Perspective,"
Econometrics Working Papers Archive
wp2008_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
- Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(1), pages 29-56, Winter.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Paper Administrator).
If references are entirely missing, you can add them using this form.