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Stochastic Processes and their Applications, ISSN 0304-4149, 11/2019, Volume 129, Issue 11, pp. 4385 - 4410
New robust estimators are introduced, derived from median-of-means principle and Le Cam’s aggregation of tests. Minimax sparse rates of convergence are... 
Robust statistics | Statistical learning | High dimensional statistics
Journal Article
Annals of Statistics, ISSN 0090-5364, 12/2012, Volume 39, Issue 4, pp. 1852 - 1877
We build penalized least-squares estimators of the marginal density of a stationary process, using the slope algorithm and resampling penalties. When the data... 
Mathematics | Statistics | Statistics Theory
Journal Article
The Annals of Statistics, ISSN 0090-5364, 8/2011, Volume 39, Issue 4, pp. 1852 - 1877
We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are β or τ-mixing,... 
Integers | Density estimation | Histograms | Mathematical theorems | Heuristics | Markov chains | Random variables | Coefficients | Estimators | Oracles
Journal Article
The Annals of Statistics, ISSN 0090-5364, 12/2016, Volume 44, Issue 6, pp. 2695 - 2725
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations... 
Fine structure | Integers | Statistical variance | Mathematical moments | Kurtosis | Random variables | Interval estimators | Estimators | Estimators for the mean | Confidence interval | Sub-Gaussian estimators | Minimax bounds | STATISTICS & PROBABILITY | minimax bounds | ADAPTIVE ESTIMATION | Statistics | Mathematics
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 07/2019, pp. 1 - 44
We obtain estimation and excess risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are... 
Learning | Risk | Statistical analysis | Outliers (statistics) | Empirical analysis | Estimators | Statistics | Statistics Theory
Journal Article
Annals of Statistics, ISSN 0090-5364, 08/2011, Volume 39, Issue 4, pp. 1852 - 1877
We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are beta or... 
Density estimation | Optimal model selection | Weak dependence | Slope heuristic | Resampling methods | slope heuristic | RISK BOUNDS | weak dependence | STATISTICS & PROBABILITY | resampling methods | PENALTIES | optimal model selection | 62M99 | 62G07 | 62G09
Journal Article
Journal of Machine Learning Research, ISSN 1532-4435, 12/2016, Volume 17, pp. 1 - 50
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2019, Volume 129, Issue 11, pp. 4385 - 4410
New robust estimators are introduced, derived from median-of-means principle and Le Cam's aggregation of tests. Minimax sparse rates of convergence are... 
Robust statistics | Statistical learning | High dimensional statistics | DENSITY | ROBUST | MODEL SELECTION | RISK | STATISTICS & PROBABILITY | ESTIMATOR | SLOPE
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 08/2012, Volume 48, Issue 3, pp. 884 - 908
In order to calibrate a penalization procedure for model selection, the statistician has to choose a shape for the penalty and a leading constant. In this... 
Density estimation | Optimal model selection | Slope heuristic | Resampling methods | CHOICE | EMPIRICAL PROCESSES | PENALIZATION | STATISTICS & PROBABILITY | PENALTIES | 62G07 | 62G09
Journal Article
The Annals of Statistics, ISSN 0090-5364, 12/2016, Volume 44, Issue 6, pp. 2533 - 2563
Journal Article
Annals of Applied Probability, ISSN 1050-5164, 06/2017, Volume 27, Issue 3, pp. 1372 - 1394
Journal Article
ESAIM: Probability and Statistics, ISSN 1292-8100, 3/2012
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 01/2018, Volume 128, Issue 1, pp. 132 - 155
We investigate the problem of estimating the cumulative distribution function (c.d.f.) F of a distribution ν from the observation of one trajectory of the... 
Adaptive estimation | Random walk in random environment | Oracle inequalities | Non-parametric estimation | MAXIMUM-LIKELIHOOD ESTIMATOR | CONSISTENCY | STATISTICS & PROBABILITY | BALLISTIC RANDOM-WALK | Statistics | Mathematics
Journal Article
ESAIM - Probability and Statistics, ISSN 1292-8100, 2012, Volume 16, Issue 1, pp. 61 - 85
We build confidence balls for the common density s of a real valued sample X-1,..., X-n. We use resampling methods to estimate the projection of s onto finite... 
Density estimation | Confidence balls | Resampling methods | REGRESSION | TESTS | MODEL SELECTION | SETS | REGIONS | STATISTICS & PROBABILITY | resampling methods | PENALTIES | density estimation | Studies | Estimating techniques | Mathematical analysis | Statistics | Asymptotic methods | Statistics Theory | Mathematics
Journal Article
Annals of Statistics, ISSN 0090-5364, 02/2019
We introduce new estimators for robust machine learning based on median-of-means (MOM) estimators of the mean of real valued random variables. These estimators... 
Statistics | Statistics Theory
Journal Article
Annals of Applied Probability, ISSN 1050-5164, 06/2017, Volume 27, Issue 3, pp. 1372 - 1394
We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely, the strengths of the players are assumed to be... 
Paired comparisons | Bradley-Terry model | Random environment | Extreme values | PAIRED-COMPARISON EXPERIMENTS | extreme values | TIES | random environment | STATISTICS & PROBABILITY | paired comparisons | Probability | Statistics | Mathematics
Journal Article
Mathematical Methods of Statistics, ISSN 1066-5307, 09/2009, Volume 18, Issue 1, pp. 59 - 83
Mathematical Methods of Statistics 18, 1 (2009) 59--83 We propose an algorithm to estimate the common density $s$ of a stationary process $X_1,...,X_n$. We... 
Statistics | Statistics Theory | Mathematics
Journal Article
08/2019
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical... 
Journal Article
Bernoulli, ISSN 1350-7265, 02/2016, Volume 22, Issue 1, pp. 325 - 344
We study the problem of estimating the one-point specification probabilities in non-necessary finite discrete random fields from partially observed independent... 
Penalization | Slope heuristic8Discrete random fields | Model selection | slope heuristic | OPTIMAL-MODEL SELECTION | model selection | penalization | STATISTICS & PROBABILITY | discrete random fields | NEIGHBORHOOD | PENALTIES | Statistics | Statistics Theory | Mathematics
Journal Article
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