Sparse estimators and the oracle property, or the return of Hodges' estimator
AbstractWe point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodgesâ estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity when ever the loss function is unbounded. For ease of presentation the result is set in the framework of a linear regression model, but generalizes far beyond that setting. In a Monte Carlo study we also assess the extent of the problem infinite samples for the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001). We find that this estimator can perform rather poorly infinite samples and that its worst-case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 142 (2008)
Issue (Month): 1 (January)
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Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- 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.
- C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
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