143 papers
This paper establishes the limiting spectral distribution of Kendall's correlation matrices in moderately high-dimensional settings with independent but non-identically distributed observations, demonstrating how distributional heterogeneity affects the spectrum and proposing a graphical tool to avoid spurious dependence detection.
This paper introduces a variational framework based on the even-odd decomposition of support functions to define geometrically interpretable size-location correlation measures for set-valued processes, establishing their statistical properties under -mixing and enabling the analysis of dependence structures that are inaccessible to traditional point-based or selection-based methods.
This paper establishes the optimal loss exponent for context-sensitive binary hypothesis testing of i.i.d. observations under a multiplicative weight function by characterizing it as a weighted Chernoff information derived from the maximization of a log-normalizer within an exponential family of weighted geometric mixtures.
This paper introduces the -footrule coefficient, a new copula-based measure of negative association defined as the -distance to the countermonotonic copula, establishes its theoretical relationship with Gini's gamma and Spearman's footrule, and provides a statistically rigorous rank-based estimator with proven consistency and asymptotic normality.
This paper develops a theory of asymptotic post-hoc inference that utilizes e-values to create sharper confidence sets and p-values with weaker assumptions than existing nonasymptotic methods, thereby allowing valid statistical conclusions even when significance levels are chosen after observing the data.
This paper addresses the point-wise and interval estimation of differential entropy for two normal populations under order-restricted prior information by deriving improved estimators that dominate the best affine equivariant estimator and comparing various confidence interval methods through numerical studies and a real-world application.
This paper resolves the non-uniqueness of maximal ancillary -fields by introducing a sequence-based asymptotic framework that enables semiparametrically efficient inference through finite-sample nuisance elimination, specifically utilizing center-outward residual ranks and signs to construct distribution-free restrictions of locally asymptotically normal experiments without requiring nuisance parameter estimation.
This paper establishes that the asymptotic distribution of quadratic forms for self-normalized heavy-tailed random vectors is determined solely by the diagonal entries of the matrix and the stability index , a result applied to derive the atom-free nature of the -heavy Marčenko--Pastur law for heavy-tailed sample correlation matrices.
This paper formalizes the goal of demonstrating positive treatment effects in adaptive experiments within a multi-armed bandit framework, proposing novel inference procedures for threshold testing and an adaptive allocation rule that optimizes signal-to-noise ratio with logarithmic regret.
This paper proposes a new goodness-of-fit test for multivariate normality that leverages -nearest neighbor estimators of Shannon entropy and Kullback-Leibler divergence to demonstrate superior power and accurate Type I error control, particularly in medium to high dimensions, compared to conventional tests.
This paper develops a thermodynamic framework for asymptotic inference that maps statistical concepts like Shannon information and parameter variance to thermodynamic entropy and state variables, revealing fundamental limits on information gain and unifying ensemble and inferential physics as opposing shadow processes.
This paper proposes Adaptive Transfer Clustering (ATC), a unified framework that automatically leverages commonalities between a main and an auxiliary dataset to improve clustering performance despite unknown discrepancies, while providing theoretical optimality guarantees under Gaussian mixture models and demonstrating effectiveness through extensive experiments.
This paper establishes criteria for determining the sign identifiability of drift coefficients in continuous-time linear stationary stochastic differential equations with known causal structures but unknown diffusion matrices, demonstrating that edge signs can be uniquely identified under faithfulness assumptions even when the full parameters cannot.
This monograph offers a rigorous theoretical and methodological overview of probabilistic inference and learning with Stein's method, detailing the construction and properties of Stein discrepancies, their connection to Stein variational gradient descent, and providing precise definitions and proofs.
This paper introduces a particle filtering framework to rigorously analyze the accuracy-cost tradeoffs of parallel inference methods in large language models, establishing theoretical guarantees and identifying fundamental limits while demonstrating that sampling error alone does not fully predict final model accuracy.
RACER is a novel, model-agnostic routing framework that addresses misrouting risks in multi-LLM systems by formulating the problem as -VOR to generate calibrated, variable-sized model sets with rigorous distribution-free risk control, thereby enhancing downstream accuracy and cost-performance trade-offs.
This paper introduces the c-delta coefficient, a novel statistical measure that quantifies the similarity of internal divergence patterns between two groups of values to assess whether their variability structures are mirrored, offering a scale-invariant tool for applications ranging from quantum physics to machine learning.
This paper establishes a rigorous framework and a convergent numerical algorithm for solving the continuous inverse problem of reconstructing a geometric -rough path from a discrete observed trajectory by formulating it as a limit of discrete inverse problems driven by piecewise linear paths.
This paper establishes the universality of high-dimensional spectral behavior and statistical limits for asymmetric rank-one spiked tensor models with non-Gaussian noise, demonstrating that the maximum-likelihood estimator's performance matches the Gaussian case under finite fourth-moment assumptions through a combination of resolvent methods, cumulant expansions, and variance bounds.
This paper establishes a law of large numbers for empirical Orlicz norms under minimal assumptions and investigates their central limit behavior, revealing that while standard convergence rates hold under specific conditions, canonical cases like the sub-Gaussian norm of normal variables exhibit nonstandard rates with stable limits, and the general class of distributions with bounded Orlicz norms admits no uniform rate of convergence.