Multi-distribution functionals reduce to integrals of coincidence divergences
Monotonicity under data processing and additivity on independent products force every such functional to an integral over four strata
math.ST
Statistics Theory
Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
Stronger backdoor triggers can raise clean accuracy in high dimensions
Proportional-regime analysis shows attack success peaks then falls while clean performance improves with training trigger strength.
· “When Stronger Triggers Backfire: A High-Dimensional Theory of Backdoor Attacks”
Gaussian limits for spectral statistics survive fourth-moment corrections
Covariance decomposition isolates a universal Gaussian term plus explicit fourth-order adjustments for linear statistics of high-dimensional
Four-plus-delta moments suffice for low-rank matrix recovery
Standard convex programs recover rank-r matrices from O(rn) heavy-tailed quadratic samples, no Gaussian assumption needed
· “Low-Rank Matrix Recovery via Heavy-Tailed Quadratic Sampling”
The experiment's randomization can estimate and test the spillover map
A design-based framework turns the known assignment into orthogonality conditions that estimate and test spillover maps.
· “A Design-Based Approach to Testing and Inference in (Quasi-)Experiments with Spillovers”
Standardizing data recovers unknown affine transforms for matching
When noise is mild, centering and scaling two noisy datasets before matching achieves the same recovery rate as if the transformation were已知
· “Exact Permutation Recovery Under Unknown Scalar Affine Transformation”
Positive Lyapunov exponent blocks natural coupling forgetfulness
Even uniformly ergodic AR models can keep memory of initial shocks under shared noise
· “Functional dependence and synchronous coupling in ergodic autoregressions”
Tree counts recover Gaussian matches at constant correlation
Poly-time algorithm succeeds for ρ² above Otter's constant whenever dimension is polylogarithmic
Screening recovers service times from workload at log/√n rate
Discrete snapshots alone suffice; no stability or arrival rate required for the L1 bound.
· “A screening approach to nonparametric inference from the M/G/1 workload”
Interleaving balls give object-level Reeb confidence
PL proximity-graph cosheaves turn sample covering radii into valid regions for the unknown filtered space
· “Building confidence regions for Reeb graphs using the interleaving distance”
Random weights turn nonnegative means into exact p-values
A 2005 conjecture is settled: one Dirichlet average is a valid finite-sample test for every mean ≤ 1
· “An Exact Distribution-Free Test for Means of Nonnegative Random Variables”
Separability tests reduce to sphericity after MLE whitening
An angular version keeps level under heavy tails without losing power when N scales with pq.
Constants turn uniformity testing into a usable SNR
The same Gaussian formula tells you the finest binning that still detects miscalibration
· “Why Constants Matter in Distribution Testing: From Uniformity to Calibration”
Geometric proof recovers sharp risk bound for basis pursuit
Facet geometry of Gaussian polytopes replaces Gaussian comparison theorems, matching the best known MSE rate for ℓ₁ interpolation
· “Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity”
Quantum toolkit cuts sample complexity for power-sum functionals from α² to α
Estimating high-order entropy functionals needs only linear-in-α samples, proven optimal via quantum primitives that yield a purely class
· “Towards Minimax Estimation of High-Order Functionals by Quantum Arguments”
No gradients needed: metric reshapes space to bridge modes
A ratio-based Riemannian metric turns exponential mode-hopping into linear cost, yielding a gradient-free sampler that mixes well on multimo
Plug-in SPMLE estimates survive non-uniqueness and nonresponse
Even when the mixing distribution can't be identified and the MLE isn't unique, functionals of it remain consistent under nonresponse.
Why self-supervised learning needs so few labels: an O(1/n) rate
Data augmentation induces a graph where label propagation achieves O(1/n_L) error, with augmentation quality entering as an explicit graph-
· “Fast Rates for Semi-Supervised Learning via Data-Augmentation Graph Regularization”
Sparse recovery rates for nonlinear inverse problems proven optimal
ℓ¹-regularized estimators achieve minimax-optimal convergence for CT and PDE inverse problems, with rates set by sparsity and spectral decay
Optimal rate found for minimizing derivatives from noisy queries
Each order of differentiation costs one unit of smoothness: the minimax rate is N^{−(β−1)/(β+k)}, matched above and below.
· “Gradient-free stochastic optimization of derivatives under strong convexity”
One randomization step unifies three families of FDR tests
Classical BH, conformal, and competition methods all reduce to a single randomized procedure with weaker assumptions
· “The Randomized BH Procedure: A Generalized Framework Encompassing Conformal and Competition Tests”
Copula density from stochastic inversion factors as base times weight
Allowing randomizers to depend on data unlocks richer copulas for non-monotone dependence
· “Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations”
Extropy of consecutive-k systems derived
An explicit uncertainty measure for reliability systems doubles as a tool to identify component distributions from system-level data
· “A Study on Cumulative Residual Extropy of Linear Consecutive k-out-of-n:G Systems”
Smaller-variance Gaussians win on convex sets above the median
A one-sided Anderson's Theorem: drop the symmetry requirement, keep the inequality whenever the reference set captures at least half the概率.
One scalar calibrates shrinkage covariance monitors across elliptical returns
Scale-invariant spectral functionals shed the kurtosis term that breaks level functionals, unifying calibration for projectors and ratio
Sparse-group LASSO beats standard LASSO for mixed-frequency panels
Combining factor extraction with group-structured penalties yields provably faster convergence for high-dimensional panel nowcasting with
One risk criterion unifies shrinkage and thresholding
A data-driven approximate risk picks between James-Stein and lasso automatically, recovering each as a special case.
· “Approximate Risk Minimization Over Shrinking-Thresholding Rules in Normal Mean Estimation”
Spectral algorithm estimates causal bilinear forms directly from staggered tensor panels
By pooling across tensor layers and targeting functionals directly, the method achieves rate-optimal error with a provable phase transition—
· “Direct and efficient estimation of bilinear forms in staggered tensor panels”
Some imprecise copulas from alternating sign matrices lose coherence
Defect transformations preserve ASMs, but only dense ASMs guarantee that a true copula fits between the bounds — a 17×17 counterexample show
· “Discrete imprecise copulas and alternating sign matrices”
Closed-form radial link replaces fitted splines in elliptical classification
Deriving the Bayes link from the generator matches tuned GAMs without smoothing selection and beats QDA on heavy-tailed data
· “Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis”
GBS step-down hits the sharp sparse-testing minimax rate
The classical step-down rule matches the best asymptotic risk under Hamming and FDP+FNP losses
Periodic test breaks focused-width conjecture by √log n
A cosine-based test detects adversarial fakes at scales far below what geometric complexity predicts, disproving a universal benchmark.
· “Focused Width in Adversarial Fake Detection: A Separation”
Edgeworth expansion for rank statistics via Stein's method and combinatorial coupling
A layered permutation construction creates enough partial independence to push Edgeworth corrections through, with error typically O(n^{-1})
· “Edgeworth Expansions for Linear Rank Statistics -- Consolidated Version”
Exact minimax risk pinned down for uniformity testing
Matching lower bound closes the constant at 2Φ(−u*/2), proving Poisson approximation is tight for multinomial testing.
CAP matches empirical risk at first order and removes second-order bias
Resampling audit plus asymptotic projection corrects over-optimism in binary classification risk estimates without sacrificing leading accur
AEW achieves T log(M)/(n+1) excess risk in expectation
The bound holds for large constant temperatures on bounded Lipschitz strongly convex losses without Bernstein assumptions
· “Aggregation with Exponential Weights is Optimal in Expectation”
Policy-coupled coverage optimizes counterfactual prediction sets
Equivalence to risk-averse optimization produces explicit optimal sets and a conformal method with finite-sample coverage guarantees.
· “Prediction Sets for Counterfactual Decisions: Coverage, Optimality, and Conformal Prediction”
Weaker matrix condition extends simplex volume theorems to AR(1) models
Central and stable limits for log-volumes of high-dimensional random simplices now hold under relaxed assumptions on the population matrix.
· “A note on "The volume of random simplices from elliptical distributions in high dimension"”
Geometric graphs indistinguishable from random above (nh(p))^3 dims
Proves conjecture by showing total variation distance to Erdős–Rényi vanishes when d ≫ (nh(p))^3 and d > n.
· “Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the d>n Regime”
Perturbation theory transfers sup-norm rates to functional principal components
L2-perturbation theory converts existing covariance kernel rates into optimal sup-norm and normality results for the associated eigenfunctio
Variational estimator beats spectral for density ratios with abundant data
In the Gaussian location model, the risk ordering reverses with the observation-to-dimension ratio under ridge regularization.
· “Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model”
Lancaster copulas arise from orthogonal expansions of Lancaster probabilities
The construction supplies infinite series for the copula and density whose low-order truncations already match target dependence in numerica
Motif signatures distinguish latent positions where degrees match
In generic finite-rank graphons, higher-order rooted patterns recover unique connectivity profiles even when degrees are identical.
· “Beyond Degree: Rooted Motif Signatures for Latent Position Identifiability in Graphon Models”
Separable graphs unify independence models in mixed graphs
Missing edges always admit separating sets, enabling canonical representations and an identification algorithm for equivalence classes
· “Characterizing and Identifying Separable Graphical Models”
Planted subgraph recovery threshold set by minimal max density
The smallest balanced induced subgraph's densest part determines when exact recovery from a random graph becomes possible with high probabil
Distributed estimator reaches two-phase minimax rates for unidentifiable prediction
Trace-similarity penalty and invex relaxation deliver model-free bounds with lower communication cost.
· “Distributed Prediction under Heterogeneity with Unidentifiable Parameter”
Three-stage estimator consistent for hybrid Lévy switching SDEs
Joint normality couples drift and scale via third moment of Lévy noise while switching rates stay uncorrelated
Worst-case top-k norm of heavy-tailed averages bounded by constants
Under variance and tail-envelope constraints the expected value is controlled up to universal factors for finite q-moment envelopes.
· “Worst-Case Maximal Inequalities for Heavy-tailed Random Vectors”
Full token observation lowers sample needs for watermark proportion estimates
Pivotal reduction to a scalar raises the number of tokens required, with matching bounds in each regime.
Marginal separable effects summarize causal effects for everyone
They stay interpretable and use routine longitudinal data instead of restricting to survivors or using composite summaries.
· “Causal Inference for All: Marginal Estimands for Outcomes Truncated by Death”
GLM formulation unifies Laplace BNN predictive estimators
Review maps exact Jacobian methods against Monte Carlo approximations and their efficiency costs.
· “A Short Review of Estimators for the GLM predictive of Laplace Bayesian Neural Networks”
Moment estimator consistent and normal for dynamic graph models
Maximum-entropy distributions on graph trajectories admit a moment-based estimator whose consistency, normality, and covariance are derived
· “Analysis of a maximum-entropy based estimator for dynamic random graph models”
Projection yields consistent payment estimators from macro insurance data
Inverse-probability weighting recovers state-specific cumulative payments under truncation and censoring
· “Payment Process Estimation in Aggregated Insurance Models”
Graph geometry and dependence set empirical rates
Maximal inequalities show convergence speed depends on function-class complexity, graph growth, and how fast dependence fades with distance.
· “Coupling and Maximal Inequalities for Graph-Dependent Empirical Processes”
Forecast sequences are auto-calibrated exactly when they form martingales
Equivalence supplies the first statistical test for calibration of updating probability predictions in any Borel space.
· “Calibrated Probability Forecast Sequences and Measure-Valued Martingales”
Optimal split minimizes conformal prediction interval length
Analytical expressions give the training-calibration ratio that shortens intervals while keeping coverage
· “On Optimal Data Splitting for Split Conformal Prediction”
Binary reduction separates error roles in minimax testing bounds
The technique produces matching lower and upper bounds for testing problems with level and type II error of different orders
FPCA rates for manifold-indexed data depend on intrinsic dimension d
Geodesic kernels with volume correction yield uniform bounds whose sparse-to-dense transition is set by manifold dimension, recovering the c
· “Functional Principal Component Analysis for Manifold-Indexed Data”
Langevin dynamics concentrate on hidden indices below temperature 1
In Gaussian multi-index models the stationary distribution forms multi-spike structures that recover parameters with high probability despit
· “The Geometry of Statistical Feature Learning in Mean-Field Langevin Dynamics”
Renyi inequalities characterize majorization of statistical experiments
Multivariate versions of these divergences supply conditions for large-sample and catalytic majorization on Borel spaces.
· “Multivariate majorization of continuous statistical experiments”
New methods enable simultaneous bands for incomplete functional time series
They handle dependence and missing sensor readings to support uniform inference over the whole domain and test for trends like high pollutio
· “Simultaneous Inference for Partially Observed Functional Time Series”
Two-stage method estimates parameters and Lévy densities in switching jumps
Small increments estimate the parametric continuous part while large residuals recover the unknown jump densities per regime.
Dual-TV regularizers bound tensor error near minimax rate
Upper bounds reach O(n3 rt sk^2 log / n) and close the gap to the lower bound by O(sk^2 / n) for exponential-family data.
· “Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularization”
Regenerative chains get data-dependent DKW bands
Leading width term uses only the sample path; convergence bound enters at lower order only
· “A data-dependent DKW inequality for regenerative Markov chains”
New method estimates largest minimizer for regression change points
Handles non-unique cases in nonparametric models where the function starts at zero and changes at an unknown point.
Minimax formulas derived for spectral densities in random-field estimation
Least favourable densities and robust estimator characteristics obtained for special admissible sets when densities are uncertain.
· “Minimax approach to the estimation problem for homogeneous random fields”
Any valid transport map is as hard to estimate as the OT map
Stability assumptions make minimax lower bounds identical for all valid maps, including those produced by diffusion and flow-matching models
· “The Fundamental Limits of Valid Transport Map Estimation”
MLE of coupling parameter consistent and efficient in hidden OU process
For a two-dimensional Ornstein-Uhlenbeck system observed in one coordinate only, the estimator achieves standard asymptotics as time horizon
· “Parameter estimation in a fully coupled partially observed Ornstein-Uhlenbeck process”
Rademacher max-average expectation bounded below by min{255/256
The inequality holds for all n and p with equality at (2,1) and (2,8); optimality of the constants is examined.
Horseshoe posterior rules attain optimal detection boundary
Decision procedures under continuous priors achieve asymptotic FDR and FNR control in sparse multiple testing
Differential algebra checks unique recovery of functions in DE models
Generalizing parameter identifiability shows when unknown components can be recovered uniquely from ideal observations.
· “Structural functional identifiability and model discovery in differential equation models”
Optimal confidence sets induce Choquet-risk optimal contours
For concentration penalties the risk reduces to expected contour volume, so levelwise optimality transfers directly to valid possibility mea
Copulas obey |β|^3 ≤ 2ξ exactly for Chatterjee ξ and Blomqvist β
The attainable pairs of these two rank correlations form the region bounded by the cubic curve |y|^3 = 2x and the line ξ = 1.
· “The exact region between Chatterjee's xi and Blomqvist's β”
Explicit MSE bounds for adaptive rare MCMC under Wasserstein contraction
Simultaneous contraction on the kernel family yields concrete error control and a cost analysis for doubly intractable targets.
· “Error bounds for simultaneous Wasserstein contractive adaptive increasingly rare MCMC”
Common noise repeats speed nonparametric regression rates
Adjusted contrast in projection estimator makes risk bounds improve with more measurements per individual.
· “Adaptive nonparametric regression from repeated measurements under common noise”
Frank-Wolfe computes optimal e-values for non-convex voting tests
Enables early stopping in sequential polls for Condorcet, Borda and Schulze systems while preserving validity.
· “Optimal Posterior E-values with Non-Convex Parameter Sets with Applications to Voting Systems”
Four Lorenz curve forms fail validity conditions
Corrected versions allow closed-form expressions for inequality measures
· “Revisiting "A universal model for the Lorenz curve with novel applications''”
Symmetric noise enables valid tests after data-driven selection
Partition data by adding and subtracting symmetric noise, then test if orthogonalization succeeds to validate the null without pre-specifyin
Multivariate BART obtains first contraction rates with joint residual dependence
Independent tree ensembles per coefficient plus a graphical horseshoe prior allow near-minimax adaptation while recovering sparse outcome ne
· “Multivariate Varying-Coefficient BART with Graphical Horseshoe Priors”
Mixture posteriors adapt to true K with extra mass vanishing at n^{-1/2}
When data follow a finite mixture, the Dirichlet process concentrates on the correct number of components, yielding nearly optimal contracti
· “Posterior concentration and adaptation of the mixing measure in Dirichlet process mixtures”