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This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer

We consider the problem of model selection and estimation in situations where the number of parameters diverges with the sample size. When the dimension is high, an ideal method should have the oracle property [J. Amer. Statist. Assoc. 96…

Statistics Theory · Mathematics 2009-08-14 Hui Zou , Hao Helen Zhang

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

Statistics Theory · Mathematics 2015-03-13 Jan Johannes , Maik Schwarz

This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…

Statistics Theory · Mathematics 2019-09-24 Evgeny Pchelintsev , Serguei Pergamenshchikov

We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…

Methodology · Statistics 2026-05-05 Omar Kassi , Sunny G. W. Wang

We discuss the problem of adaptive discrete-time signal denoising in the situation where the signal to be recovered admits a "linear oracle" -- an unknown linear estimate that takes the form of convolution of observations with a…

Statistics Theory · Mathematics 2021-02-15 Zaid Harchaoui , Anatoli Juditsky , Arkadi Nemirovski , Dmitrii Ostrovskii

We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…

Methodology · Statistics 2017-10-31 Felix Abramovich , Daniela De Canditiis , Marianna Pensky

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve…

Optimization and Control · Mathematics 2023-10-10 Mustapha Kaci , Sonia Radjef

We tackle the problem of estimating a regression function observed in an instrumental regression framework. This model is an inverse problem with unknown operator. We provide a spectral cut-off estimation procedure which enables to derive…

Statistics Theory · Mathematics 2009-01-28 Jean-Michel Loubes , Clément Marteau

In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy…

Numerical Analysis · Mathematics 2022-02-28 Tim Jahn

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two…

Statistics Theory · Mathematics 2007-06-13 T. Tony Cai , Mark G. Low

Empirical research typically involves a robustness-efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they…

Econometrics · Economics 2025-09-17 Timothy B. Armstrong , Patrick Kline , Liyang Sun

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…

Statistics Theory · Mathematics 2015-04-08 Niels Richard Hansen , Patricia Reynaud-Bouret , Vincent Rivoirard

In the presence of a missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. When the population totals of some auxiliary variables are known and when the…

Methodology · Statistics 2014-10-16 Kwun Chuen Gary Chan , Sheung Chi Phillip Yam

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…

Machine Learning · Statistics 2012-10-22 Alexandra Carpentier , Rémi Munos

In this paper, we study the problem of pointwise estimation of a multivariate density. We provide a data-driven selection rule from the family of kernel estimators and derive for it a pointwise oracle inequality. Using the latter bound, we…

Statistics Theory · Mathematics 2015-09-21 Gilles Rebelles

We consider the problem of adaptive estimation of the regression function in a framework where we replace ergodicity assumptions (such as independence or mixing) by another structural assumption on the model. Namely, we propose adaptive…

Statistics Theory · Mathematics 2010-11-03 Sylvain Delattre , Stéphane Gaïffas

This paper presents a novel approach for pointwise estimation of multivariate density functions on known domains of arbitrary dimensions using nonparametric local polynomial estimators. Our method is highly flexible, as it applies to both…

Statistics Theory · Mathematics 2025-07-22 Karine Bertin , Nicolas Klutchnikoff , Frédéric Ouimet

In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of…

Machine Learning · Computer Science 2018-08-28 Max Simchowitz , Kevin Jamieson , Jordan W. Suchow , Thomas L. Griffiths

Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with…

Statistics Theory · Mathematics 2008-11-10 A. Juditsky , P. Rigollet , A. B. Tsybakov