Probability & Statistics · Mathematics & Statistics
Statistics Theory
The newest papers in Statistics Theory that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
321 papers, from 31 August 2026 to 4 November 2026: 287 arXiv preprints and 34 OpenAlex records.
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Newest papers, page 6
Pathwise Shrinkage and Probabilistic Calibration of the Multiplicative Half-Cauchy Process
We characterize the multiplicative half-Cauchy process through its log-scale random-walk representation, establishing shrinkage, expansion, and critical regimes, almost-sure summability, local…Regret Lower Bound for Online Learning of Quantum States with Logarithmic Loss, with Applications to Quantum State Tomography and Confidence Sequences for Matrix Means
We study the problem of online learning of quantum states with logarithmic loss, which is a quantum generalization of online portfolio selection and has applications to quantum state tomography, the…Dimension-Free PAC-Bayes Generalization for Deep Neural Networks via Dirichlet Processes
Classical PAC-Bayesian generalization theory places prior distributions over Euclidean parameter space $Θ\subseteq \mathbb{R}^D$, causing relative entropy to scale with network dimension $D$.Two Sample Sizes in Test-Time LLM Ensembling: Buffered ERM and Minimax Theory
Test-time scaling can improve the performance of large language models by generating multiple answers to a question and aggregating them.Asymptotic Behavior of Transformers
In this paper we study the behavior of transformer networks generating text over long periods of time.On Inherent Privacy of Posterior Sampling: A Unified Rényi-Divergence Framework
Differential Privacy (DP) provides a rigorous framework for quantifying privacy guarantees.Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds
We study the minimax estimation of the pseudo-spectral gap $γ_{ps}$ of a Markov chain from the observation of a single trajectory.MCMC Can See Can't See
It is folklore that passing "convergence" diagnostics does not guarantee that a Markov chain has converged.Stochastic Gradient Descent: A Nonlinear Time Series Perspective
This paper investigates the statistical behavior of Stochastic Gradient Descent (SGD) with constant step size under the framework of iterated random functions.Two-Stage Score Estimation for Group-Specific Diffusion Models
Generative modeling across related distributions raises a question: how can shared structure support accurate generation for a target distribution with limited observations?textGrain watermarking is harder to detect: can sum-tests still do it optimally?
Watermarking embeds an imperceptible signal in text from large language models that is statistically detectable with a secret key.Minimax rates for pointwise CATE estimation: the role of design smoothness
We study the role of design smoothness in the minimax estimation of conditional average treatment effects at a fixed covariate point.Optimal Support Size Testing
We present an optimal tester for support size that determines whether an unknown probability distribution is supported on $n$ elements or $\varepsilon$-far away (in total variation distance) with…Finite-sample certification of coverage regret for budgeted document selection under adaptive stratified auditing
Selecting a budget-constrained set of documentary fragments, for instance the knowledge base of a retrieval-augmented generation system, raises a statistical question: how much expected query…Limit Theory for Online Expectile Estimation under Short and Long Range Dependence
Expectiles are tail-sensitive distributional summaries with important applications in financial risk measurement and forecasting, yet statistical theory for their online estimation from dependent…Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks
This paper develops a unified framework for distributional regression with arbitrary response variables.Reflected Proximal Dynamics for Accelerated High-Accuracy Log-Concave Sampling
We study sampling from $π(x)\propto\mathrm{e}^{-V(x)}$ on $\mathbb{R}^d$, where $V$ is $α$-strongly convex and $β$-smooth with condition number $κ=β/α$.Graph Matching in Random Geometric Graphs I: Efficient Algorithms
We study the recovery of the hidden vertex correspondence between two correlated dense random geometric graphs.Spectral Costs of Multinomial and Residual Resampling in High-Dimensional Particle Ensembles: A Free-Probability Analysis
Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood.Explicit Bounds on Hoffman Constants for Sparse Polyhedral Regularizers
Hoffman constants quantify the distance to the solution set of a polyhedral system in terms of its residual; they control error bounds, geometric conditioning, the convergence rate of first-order…