Approximation dans les espaces métriques et théorie de l'estimation

By Lucien Birgé. 1983

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Citations in the corpus

The semiparametric Bernstein-von Mises theorem (2010, methodology): “To find sufficient conditions, we follow a construction of tests based on the Hellinger geometry of the model, generalizing the approach of Birgé [2, 3] and Le Cam [30] to n−1/2-perturbed context.”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, background): “c being some universal constant (for similar results in the context of density estimation with Hellinger loss, see [8], p.”
Nonparametric Bayesian model selection and averaging (2008, background): “[2000], LeCam [1973] and Birgé [1983] on the existence of tests of certain tests under local entropy of a statistical model.”
On minimax density estimation on R (2001, background): “(Birgé 1983)).”
Wavelet Shrinkage: Asymptopia? (1995, methodology): “[2] No method can exceed the rate (n ): for some other constant C2(k k;F)”
On the Frequentist Properties of Bayesian Nonparametric Methods (2016, methodology): “Birgé, 1983.”
Covering Numbers for Convex Functions (2012, background): “Our results have direct implications in this regard in the context of understandingthe rates of convergence of the numerous convexity constrained function estimators, e.g., the nonparametric least squares estimator of a convex regression function studied in [11], [12]; the maximum likelihood…”
Local Privacy, Data Processing Inequalities, and Statistical Minimax Rates (2013, background): “We thus obtain the local Fano lower bound [36, 8] on the classical minimax risk:”
ADAPTIVE ESTIMATION OF A QUADRATIC FUNCTIONAL BY MODEL SELECTION (2001, background): “Indeed, when estimating the function itself with various loss functions, one can identify the order of the minimax risk in terms of the metric dimension of [see the landmark paper by Birg´e (1983) on this topic].”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, methodology): “This fact is rooted in the subtle connection between nonparametric testing problems and the Hellinger metric as highlighted in the work of Le Cam [21] and Birgé [2].”
Information-theoretic lower bounds on the oracle complexity of convex optimization (2009, methodology): “With this set-up, we are able to apply the Fano lower bound for statistical estimation, as has been done in past work on nonparametric estimation (e.g., [5, 2, 11]).”
Minimax Rates of Estimation for High-Dimensional Linear Regression Over q -Balls (2009, result): “[5, 18, 39]) with results in the approximation theory literature (e.”