Topics in Non-Parametric Statistics

By Arkadi Nemirovski. 2000

281 citations recorded by the source corpus.

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Citations in the corpus

Learning Distributions from their Samples under Communication Constraints (2019, background): “2) Non-parametric distributions: in this case X 1 , X 2 , · · · , X n i.i.d. ∼ f , where f is a density that possesses some standard H¨older continuity property [18].”
Exponential Screening and optimal rates of sparse estimation (2010, methodology): “Nemirovski (2000) Note that all these sets Θ are of the form B 0 ( S ) ∩ B 1 ( δ ) for speciﬁc values of S and δ .”
SPADES AND MIXTURE MODELS (2009, background): “We would like to cover more general problems where the system {fj} is not necessarily orthonormal, even not necessarily a basis, M is not necessarily smaller than n, but an estimate of the form fbλ still achieves, adaptively, the optimal rates of convergence.”
MINIMAX ESTIMATION OF A FUNCTIONAL ON A STRUCTURED (2016, methodology): “The methods connect to earlier work [10, 18] on the estimation of functionals on nonparametric models, but differ by our focus on functionals that are defined in terms of the structure of a semiparametric model.”
Model selection via testing: an alternative to (penalized) maximum likelihood estimators (2006, methodology): “The method also applies to Gaussian sequences if we duplicate our observation according to the recipe of Chapter 6 of Nemirovski [50].”
Minimax Estimation of Functionals of Discrete Distributions (2014, unknown): “[74] pioneered the use of approximation theory in functional estimation in the Gaussian white noise model (see Nemirovski [75] for a comprehensive treatment).”
User-friendly introduction to PAC-Bayes bounds (2021, methodology): “Many aggregates share a formal similarity with the EWA of online learning and with the Gibbs posterior of the PAC-Bayes approach, we refer the reader to [144, 106, 202, 139, 203, 42, 206, 119, 116, 64, 40, 183, 65, 60, 63, 59, 62, 126, 61].”
Sharp adaptation for inverse problems with random noise (2002, methodology): “It uses the techniques of Nemirovskii (1998), Section 6.3.3.”
Gaussian model selection (2001, methodology): “…by Kerkyacharian and Picard (see, for instance, Kerkyacharian and Picard, 2000 and the references therein), Lepskii’s method starting with Lepskii (1990, 1991) and adaptive local polynomial fit as initiated by Katkovnik (1979) (see a detailed account and recent developments in Nemirovski, 2000).”
Exact minimax risk for linear least squares, and the lower tail of sample covariance matrices (2019, background): “By contrast, in the linear aggregation problem as defined by [51] (and studied by [71, 15, 13, 5, 33, 41, 49, 53]), one seeks to obtain excess risk bounds, also called exact oracle inequalities (where the constant 8 in the bound (1.”
Goodness-of-fit testing and quadratic functional estimation from indirect observations (2006, background): “Nemirovski [25] gave asymptotically efficient estimators of less smooth functionals, one or two times continuously differentiable.”
Linear and convex aggregation of density estimators (2006, methodology): “…ﬁrst analysis we will not consider sample splitting schemes but rather deal with a “pure aggregation” framework (as in most of the papers on the subject, cf. ,e.g., Nemirovski (2000), Juditsky and Nemirovski (2000) and Tsybakov (2003) for the regression problem) where the ﬁrst subsample is frozen.”