Deux remarques sur l'estimation

By P. Assouad. 1983

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Citations in the corpus

Learning discrete distributions: user vs item-level privacy (2020, methodology): “We generalize Assouad’s lemma [Assouad, 1983, Yu, 1997] with diﬀerential privacy and the restricted estimators using the recent coupling methods of Acharya et al. [2018, 2020].”
Optimal Schemes for Discrete Distribution Estimation Under Locally Differential Privacy (2017, methodology): “In the classical (non-private) minimax estimation problem, one standard approach to the proof of lower bounds on the minimax risk of estimation is Assouad’s method [18] (see also [19]).”
Minimax Optimal Procedures for Locally Private Estimation (2016, methodology): “Letting P ± j denote the joint distribution over the random index V and X conditional on the j th coordinate V j = ± 1, we obtain the following sharper variant of Assouad’s lemma (Assouad 1983).”
Memory, Communication, and Statistical Queries (2016, methodology): “In this section, we complement this result with a more direct communication lower bound based on Assouad’s method [Assouad, 1983] that applies to the streaming model of bounded communication.”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “Then xω2(x) is increasing from 0 to ω2(1) and, if μ is the Lebesgue measure, it follows from classical lower bounds arguments based on Assouad’s Lemma (see [1,11] or [74]) that, for an n-sample and μ the uniform distribution, the minimax risk R(Sω,2) is bounded from below by”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, methodology): “The result can be viewed as a generalization of Le Cam’s method in one direction and Assouad’s lemma in another. This new technical tool is useful for a range of other estimation problems. For example, it was used in Cai et al. (2012) for establishing the optimal rate of convergence for estimating s”
Optimal schemes for discrete distribution estimation under local differential privacy (2017, methodology): “In the classical (non-private) minimax estimation problem, lower bounds on the risk are derived using Assouad’s method [15].”
On the Fundamental Limits of Adaptive Sensing (2011, result): “2The main ideas of our proof are similar to those in that of Assouad’s Lemma, see [8] and [29], for instance.”
Smooth Discrimination Analysis (1999, background): “We show that, under assumptions on the "-entropy of the class of possible sets G , the empirical risk minimization rules of Vapnik and Cervonenkis (1974) type converge with optimal rate, in the distance df;g and in the distance d [Lebesgue measure of symmetric di erence, see (1) below].”
Optimal estimation of the mean function based on discretely sampled functional data: Phase transition (2011, methodology): “For each b = ( b 1 , . . . , b 2 m ) ∈ { 0 , 1 2 m , deﬁne The claim then follows from an application of Assouad’s lemma [Assouad (1983)].”
Lower Bounds for Locally Private Estimation via Communication Complexity (2019, methodology): “in minimax lower bounds, which build out of work by Zhang et al. [37], Garg et al. [17], and Braverman et al. [5] on communication limits in estimation. We begin with an extension of Assouad’s method [2,36], which transforms a d-dimensional estimation problem into one of testing dbinary hypotheses, ”
MINIMAX ESTIMATION OF LARGE COVARIANCE MATRICES UNDER ℓ1-NORM (2012, methodology): “We establish the lower bound (16) by using Assouad’s Lemma and the lower bound (17) by using a version of Fano’s Lemma given in Tsybakov (2009). 2.2.1 Proof of the lower bound (16) The key technical tool to establish (16) is the lemma in Assouad (1983). It gives a lower bound for the maximum risk ov”
On Bayes Risk Lower Bounds (2014, background): “The total variation distance appears in many classical minimax bounds including the well-known inequalities due to Le Cam (1973) and Assouad (1983).”
A ug 2 01 4 Local Privacy , Data Processing Inequalities , and Minimax Rates (2018, methodology): “Letting P±j denote the joint distribution over the random index V and Z conditional on the jth coordinate Vj = ±1, we are able to establish the following sharpening of Assouad’s lemma [5, 4] (see Appendix F.”