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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? Learning Perturbations to Extrapolate Your LLM Byzantine-Robust Distributed Sparse Learning Revisited The Sample Complexity of Multiple Change Point Identification under Bandit Feedback A proximal gradient algorithm for composite log-concave sampling Model-based Bootstrap of Controlled Markov Chains Approximation of Maximally Monotone Operators : A Graph Convergence Perspective Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces MIST: Reliable Streaming Decision Trees for Online Class-Incremental Learning via McDiarmid Bound A Spectral Framework for Closed-Form Relative Density Estimation Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation Scaling Limits of Long-Context Transformers A Note on Non-Negative $L_1$-Approximating Polynomials Susceptibilities and Patterning: A Primer on Linear Response in Bayesian Learning Linear Response Estimators for Singular Statistical Models Statistical inference with belief functions: A survey Robust stochastic first order methods in heavy-tailed noise via medoid mini-batch gradient sampling Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexity Adaptive auditing of AI systems with anytime-valid guarantees Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions Risk-Controlled Post-Processing of Decision Policies Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning A Unified Pair-GRPO Family: From Implicit to Explicit Preference Constraints for Stable and General RL Alignment Time-Inhomogeneous Preconditioned Langevin Dynamics A Fine-Grained Understanding of Uniform Convergence for Halfspaces CITE: Anytime-Valid Statistical Inference in LLM Self-Consistency Ratio-based Loss Functions Optimal Confidence Band for Kernel Gradient Flow Estimator A renormalization-group inspired lattice-based framework for piecewise generalized linear models
Une alternative robuste au maximum de vraisemblance: la $...
Yannick Baraud, Lucien Birgé · 2017-03-06 · via math.ST updates on arXiv.org

This paper is based on our personal notes for the short course we gave on January 5, 2017 at Institut Henri Poincaré, after an invitation of the SFdS. Our purpose is to give an overview of the method of $ρ$-estimation and of the optimality and robustness properties of the estimators built according to this procedure. This method can be viewed as the sequel of a long series of researches which were devoted to the construction of estimators with good properties in various statistical frameworks. We shall emphasize the connection between the $ρ$-estimators and the previous ones, in particular the maximum likelihood estimator, and we shall show, via some typical examples, that the $ρ$-estimators perform better from various points of view. ------ Cet article est fondé sur les notes du mini-cours que nous avons donné le 5 janvier 2017 à l'Institut Henri Poincaré à l'occasion d'une journée organisée par la SFdS et consacrée à la Statistique Mathématique. Il vise à donner un aperçu de la méthode de $ρ$-estimation ainsi que des propriétés d'optimalité et de robustesse des estimateurs construits selon cette procédure. Cette méthode s'inscrit dans une longue lignée de recherches dont l'objectif a été de produire des estimateurs possédant de bonnes propriétés pour un ensemble de cadres statistiques aussi vaste que possible. Nous mettrons en lumière les liens forts qui existent entre les $ρ$-estimateurs et ces prédécesseurs, notamment les estimateurs du maximum de vraisemblance, mais montrerons également, au travers d'exemples choisis, que les $ρ$-estimateurs les surpassent sur bien des aspects.