PERFORMANCE LIMITS FOR ESTIMATORS OF THE RISK OR DISTRIBUTION OF SHRINKAGE-TYPE ESTIMATORS, AND SOME GENERAL LOWER RISK-BOUND RESULTS

By H. Leeb, B. M. Potscher. Econometric Theory, 2005

59 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d2ad1879e602790d5bc1e23c3ceabbf378c172fa

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In Management Science and Operations Research

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Citations in the corpus

Valid post-selection inference (2013, unknown): “…specific problems have been the subject of incisive analyses and criticisms by the “Vienna School” of Pötscher, Leeb and Schneider; see, for example, Leeb and Pötscher (2003, 2005, 2006a, 2006b, 2008a, 2008b, 2008c), Pötscher (2006), Leeb (2006), Pötscher and Leeb (2009), Pötscher and…”
On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection (2006, methodology): “The first term in (B.1) can be expressed using the weighted cdf (A.1) with s = ±tα/2 and with r(P) replacing r or, equivalently, using expression (A.2) with s = ±tα/2 [because the weighted cdf in (A.2) is continuous].”
Comparison of Volatility Measures: A Risk Management Perspective (2010, unknown): “As a result of the ill–conditioned Hessian, cubic splines tend to adapt 4As with other parameter reduction techniques there are problems with inference as Leeb & Pötscher (2006) pointed out that the risk of PML estimator cannot be uniformly consistently estimated (see also Hurvich & Tsai (1990)).”
Uniformly valid confidence intervals post-model-selection (2016, background): “…of valid statistical procedures in such situations is quite challenging, even if the candidate set of models does contain the true distribution (cf. Leeb and Pötscher (2005, 2006, 2008), Kabaila and Leeb (2006) and Pötscher (2009), and the references given in that literature), and has recently…”
Bootstrapping Lasso Estimators (2011, methodology): “In context to the consistency result presented in Theorem 1, it is important to mention the interesting work done by Pötscher and coauthors (Leeb and Pötscher 2006; Leeb and Pötscher 2008; and Pötscher and Schneider 2009), who have studied the (uniform) consistency of estimates of distributions…”
ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP (2009, background): “…include Loh (1985), Gleser and Hwang (1987), Sen and Saleh (1987), Stock (1991), Cavanagh, Elliot, and Stock (1995), Hall and Jing (1995), Kabaila (1995), Dufour (1997), Staiger and Stock (1997), Pötscher (2002), Anatolyev (2004), Imbens and Manski (2004), and Leeb and Pötscher (2005, 2006).”
On the distribution of the adaptive LASSO estimator (2008, unknown): “…stress that the above result also applies to any kind of bootstrap-or subsampling-based estimator of the cdf F A,n,θ whatsoever, since the results in Leeb & P¨otscher (2006b) on which the proof of Theorem 11 rests apply to arbitrary randomized estimators, cf. Lemma 3.6 in Leeb & P¨otscher (2006b).”
CAN ONE ESTIMATE THE UNCONDITIONAL DISTRIBUTION OF POST-MODEL-SELECTION ESTIMATORS? (2007, unknown): “Bauer, Pötscher, and Hackl (1988)) the (pointwise) asymptotic distribution is always normal. [This is elementary, cf. Lemma 1 in Pötscher (1991).] However, as discussed at length in Leeb and Pötscher (2005a), this asymptotic normality result paints a misleading picture of the nite sample distribut”
Donsker-type theorems for nonparametric maximum likelihood estimators (2007, background): “3 in [19] for a general study of such problems.”
Model Selection (2018, methodology): “Of course, model averaging methods have also been analyzed from a frequentist perspective; see, for example, Buckland, Burnham, and Augustin (1997), Magnus (2002), Juditsky and Nemirovski (2000), Yang (2001, 2003), Hjort and Claeskens (2003), Danilov and Magnus (2004), Leung and Barron (2006), as we”
LASSO-TYPE GMM ESTIMATOR (2009, background): “As discussed in Leeb and Pötscher (2006), none of the postselection estimators display very good finite-sample properties, and neither does the Lasso.”
Unified LASSO Estimation by Least Squares Approximation (2007, result): “These results further confirm the theoretical findings of Leeb and Pötscher (2005) stating that no consistent model selection method including LSA can have a good minimax efficiency.”
Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators (2009, background): “The results of Leeb and Pötscher (2006) show that no uniformly consistent estimator of the distribution of a super-efficient estimator exists.”