2007/04/11 by Hannes Leeb, Benedikt M. Pötscher, Benedikt M. Poetscher · 6 citations
Mathematics · #Advanced Causal Inference Techniques #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #math.ST #msc:62C99 #msc:62E20 #msc:62F10 #msc:62F12 #msc:62J07 #stat.ME #stat.TH
paper · pdf · doi:10.1016/j.jeconom.2007.05.017
published as Journal of Econometrics (2008) · 18 pages, 5 figures
arxiv created 2007/04/11 · openalex publication_date 2007/06/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 whenever 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 in finite samples for the smoothly clipped absolute deviation (SCAD) estimator introduced in Fan and Li (2001). We find that this estimator can perform rather poorly in finite samples and that its worst-case performance relative to maximum likelihood deteriorates with increasing sample size when the estimator is tuned to sparsity.