Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator

Hannes Leeb () and Benedikt M. Poetscher
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Benedikt M. Poetscher: Dept. of Statistics, University of Vienna
Authors registered in the RePEc Author Service: Benedikt M. Pötscher

No 1500, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We 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 Hodges’ 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.

Keywords: Oracle property; Sparsity; Penalized maximum likelihood; Penalized least squares; Hodges’ estimator; SCAD; Lasso; Bridge estimator; Hard-thresholding; Maximal risk; Maximal absolute bias; Non-uniform limits (search for similar items in EconPapers)
JEL-codes: C20 C51 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2005-02, Revised 2007-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (14)

Published in Journal of Econometrics (2008), 142: 201-211

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Journal Article: Sparse estimators and the oracle property, or the return of Hodges' estimator (2008)
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