Convergence of Estimates Under Dimensionality Restrictions

By L. Lecam. 1973

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness (2020, background): “It is worth noting that the Laplace approximation to the RFF posterior is asymptotically exact by the virtue of the Bernstein-von Mises (BvM) theorem and the fact that (3) is a finite-rank model (Dehaene, 2019; Freedman, 1999; LeCam, 1973; Panov and Spokoiny, 2015).”
The hardness of conditional independence testing and the generalised covariance measure (2018, neutral): “lim inf n→∞ inf Q∈QQn = 1) < 1, [33], [4], Proposition 2, Theorem 3.”
Rényi Divergence and Kullback-Leibler Divergence (2012, background): “…divergence, Kullback-Leibler divergence, Pythagorean inequality, Rényi divergence I. INTRODUCTION SHANNON entropy and Kullback-Leibler divergence (alsoknown as information divergence or relative entropy) are perhaps the two most fundamental quantities in information theory and its applications.”
Minimax Optimal Procedures for Locally Private Estimation (2016, methodology): “The classical version of Le Cam’s method bounds the (nonpri-vate) minimax risk (1) in terms of a two-point hypothesis testing problem (Le Cam 1973; Yu 1997; Tsybakov 2009).”
The Right Complexity Measure in Locally Private Estimation: It is not the Fisher Information (2018, methodology): “In this case, a number of tools are available, but to keep our presentation tighter, we focus on the generalized version of Le Cam’s method [33, 56].”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “As Le Cam said in the introduction of this paper, " one of the most widely used methods of statistical estimation is that of maximum likelihood . . . . Qualms about the general validity of optimality properties (of maximum likelihood estimators) have been expressed occasionally.”
Lower bounds for non-convex stochastic optimization (2019, background): “Proof of Lemma 11 The proof follows standard arguments used to derive informationtheoretic lower bounds for statistical estimation [31, 54].”
Differentially Private Assouad, Fano, and Le Cam (2020, methodology): “The first term in Theorem 1 follows from the classic Le Cam’s method (Lemma 1 in Yu (1997)).”
Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional (2011, methodology): “See, for example, Le Cam (1973) and Donoho and Liu (1991).”
Optimality guarantees for distributed statistical estimation (2014, background): “This result is based on the classical reduction from estimation to testing (e.g., [21, 19, 6]).”