Minimax Estimation

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Overview

Minimax estimation asks how accurately an unknown quantity can be recovered in the hardest case within a specified model, and how many observations are needed. Researchers establish upper bounds for concrete estimators and lower bounds that apply to every method, often using regularization, aggregation, thresholding, and information-theoretic tools such as Fano's and Le Cam's methods. The framework covers settings including nonparametric regression, sparse covariance and distribution estimation, one-bit data, dependent observations, and differential privacy. A central challenge is understanding when adaptation to unknown structure is possible without extra cost, especially when privacy, contamination, or computational limits change the achievable rates.

Latest papers

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94 papers23 papers in the last four weeks, up 92% on the four weeks before. 0.1% of all new papers.

  1. The Cost of Working Memory in Streaming Mean Estimation

    Oct 29, 2026Zeyu Wu, Zihao Wang, Minghua DengStreaming AlgorithmsMinimax Estimation

  2. Pair-Dependent Judge Errors Change the Minimax Rate of Semantic Entropy

    Oct 29, 2026Jiamiao Liu, Dewen Qiao, Yu Zhang +1Semantic EntropyMinimax Estimation

    Department of Information, Xinqiao Hospital Army Medical University (Third Military Medical University) Chongqing 400037, China

  3. Approximation Families and the Statistical Efficiency of Denoising Score Matching

    Oct 26, 2026Brian MiyatakeScore MatchingScore-Based Generative Modeling

    Department of Statistics and Data Science, Yale University

  4. Exact Global Minimax Risk near Nonidentification

    Oct 23, 2026Kaiyue Yang, Yunan WuMinimax EstimationParameter Identifiability

    Qiuzhen College, Tsinghua University, Haidian District, Beijing 100084, P. R. China · Yau Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing 100084, P. R. China

  5. Minimax Optimality of the NPMLE for Gaussian Mixtures in Hellinger Distance

    Oct 21, 2026Shayan Hundrieser, Tudor ManoleGaussian Mixture ModelsMinimax Estimation

    Department of Statistics and Data Science, Yale University · Department of Statistics, Stanford University

  6. The Price of Current-Effect Inference in Nonstationary Multi-Armed Bandits

    Oct 21, 2026Sharan Sahu, Martin T. WellsNon-Stationary BanditsDynamic Regret Minimization

    Department of Statistics and Data Science, Cornell University

  7. Near Minimax Rate for Quantile Distributional Reinforcement Learning

    Oct 21, 2026Zijie Cheng, Zhihua ZhangDistributional RLPolicy Evaluation

    School of Mathematical Sciences, Peking University

  8. Solving the Ho--Nguyen Conjecture for Gaussian Mixtures: Applications to Mixtures of Experts

    Oct 19, 2026Yuyang Zhang, Qihuang ZhangGaussian Mixture ModelsParameter Identifiability

    McGill University

  9. Robust Latent Variable Graphical Models: Exact Recovery and Fundamental Limits

    Oct 19, 2026Chuansen Peng, Xiaojing ShenRobust EstimationGraph Structure Learning

    School of Mathematics, Sichuan University, Chengdu 610064, China

  10. Query-Dependent Reading for Quantized Inner-Product Estimation: A Minimax Separation

    Oct 17, 2026Krishnakumar Balasubramanian, Siddharth Bhandari, Shiva Prasad KasiviswanathanQuantizationMinimax Estimation

    Amazon* · Department of Statistics, University of California, Davis

  11. Minimax-optimal Scaling Laws in Ridge Regression via Transfer Learning

    Oct 16, 2026Yalda Shabanzadeh, Diyuan Wu, Marco MondelliTransfer LearningRidge Regression

    Institute of Science and Technology Austria (ISTA).

  12. Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds

    Oct 14, 2026Vahe Karagulyan, Mikołaj Kasprzak, Pierre AlquierMarkovian BanditsMinimax Estimation

    ESSEC Business School

  13. Discrete Diffusion Models are Minimax Optimal Under Sparsity

    Oct 13, 2026Luca Blunda, Tyler Farghly, Umut Simsekli +1Diffusion ModelsMinimax Estimation

    INRIA - École Normale Supérieure - PSL Research University - CNRS, France · École Polytechnique - CMAP - IP Paris, France

  14. Minimax rates for pointwise CATE estimation: the role of design smoothness

    Oct 13, 2026Yuxuan Hou, Zhenghan LiConditional Average Treatment Effect EstimationMinimax Estimation

    Qiuzhen College, Tsinghua University · School of Statistics, University of Minnesota

  15. Recalibrating Many Questions with Few Labels: Minimax Rates and Identification Limits

    Oct 13, 2026Xiaoyu Li, Chiwun YangProbability CalibrationMinimax Estimation

    University of New South Wales. · City University of Hong Kong.

  16. Rarity Determines Minimax Rates of Semantic Entropy From Weak Pairwise Judgments With a Known Channel

    Oct 13, 2026Xiaoli Yu, Jiamiao LiuSemantic EntropyMinimax Estimation

    School of Cyber Security and Information Law, Chongqing University of Posts and Telecommunications, Chongqing 400065, China · Department of Information, Xinqiao Hospital, Army Medical University (Third Military Medical University), Chongqing 400037, China

  17. Minimax Rates and Improved Spectral Convergence for Multi-Manifold Clustering

    Oct 11, 2026Haoyu Chen, Chenghui LiManifold LearningMinimax Estimation

    Department of Statistics University of Wisconsin Madison Madison, WI 53706, USA

  18. Sparsity Saves Compute, Not Samples: Oracle Inequalities for Dense and Sparse Mixture of Experts

    Oct 10, 2026Sagar Ghosh, Huy Nguyen, Alessandro RinaldoSparse Mixture-of-ExpertsMixture-of-Experts Models

    The University of Texas at Austin

  19. Minimax Rates for Estimating Powered Sliced Wasserstein Functionals

    Oct 8, 2026Binh Thuan TranMinimax EstimationSliced Wasserstein Distance

    LAMA, LIGM, Université Gustave Eiffel

  20. Subspace Uncertainty and Sharp Sampling Thresholds on the Boolean Cube

    Oct 8, 2026Thomas WeinbergerSample ComplexityStatistical Learning Theory

    School of Computer and Communication Sciences, EPFL, Switzerland

  21. Holdout Best-of-N: Unbiased Evaluation and Its Cost

    Oct 6, 2026Shrey Shah, Yinheng LiBest-of-N SamplingPolicy Evaluation

  22. Detecting a Shift Is Not Enough: Exact Minimax Limits of Linear Representation Repair

    Oct 6, 2026Anuar Aimoldin, Yankai Chen, Ayana Mussabayeva +1Distribution Shift RobustnessMinimax Estimation

    Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)

  23. Uniform Discrete Diffusion Models are Minimax Optimal for Estimating Distributions with Small Effective Support Size

    Oct 6, 2026Dongsun Yoon, Saptarshi ChakrabortyMinimax EstimationStatistical Learning Theory

    Department of Statistics, University of Michigan

  24. Assumption-lean logistic regression with missing covariates

    Oct 5, 2026Jyotishka Ray Choudhury, Kabir Aladin Verchand, Richard J. Samworth +1Logistic RegressionLearning with Missing Data

    School of Industrial and Systems Engineering, Georgia Institute of Technology · Department of Data Sciences and Operations, University of Southern California · Statistical Laboratory, University of Cambridge +1

  25. Minimax Additive Regression under Unknown Dependent Designs

    Sep 30, 2026Baptiste Ferrere, Fabrice Gamboa, Jean-Michel LoubesNonparametric RegressionMinimax Estimation

    Université de Toulouse EDF R&D · Université de Toulouse ANITI

  26. Minimax rates for learning spectral Barron functions by deep ReLU neural networks

    Sep 30, 2026Songqiu Ma, Yunfei YangReLU Neural NetworksMinimax Estimation

    School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, China. · School of Mathematics (Zhuhai) and Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Zhuhai, China.

  27. Sharp Limits for Honest Uncertainty in Hard-Budget Repeated Evaluation

    Sep 24, 2026Yezhou Cheng, Runjia Du, Zeming Liu +5Confidence Region EstimationUncertainty Quantification

    Independent · Northwestern University · Pinterest, Inc.

  28. Error Bounds for Statistical Estimators in BTL Model with Parametric Multivariate Utility Functions

    Sep 22, 2026Yicheng Li, Huifu XuParameter EstimationMinimax Estimation

    Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong.

  29. Statistical Gains from Looped Estimation under Parameter Budgets

    Sep 22, 2026Xinyu Tian, Xiaotong ShenParameter EstimationParameter Sharing

    School of Statistics, University of Minnesota

  30. Optimal Tradeoffs Between Network Size and Parameter Magnitude in Neural Approximation and Minimax Regression

    Sep 22, 2026Baicheng Li, Zuowei Shen, Haizhao Yang +1Neural Network OptimizationNonparametric Regression

    Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA. · Department of Mathematics, National University of Singapore, Singapore 119076. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.