Statistics Theory
stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
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Minimum free energy randomization controls imbalance and prevents unobserved factors from dominating error in effect estimates
· “Minimum free energy randomized design to improve covariate balance”
Review shows how tail models support regression, classification, dimension reduction and anomaly detection in rare-event settings.
· “Extrapolation in Statistical Learning with Extreme Value Theory”
Two-gradient scheme matches prior convergence guarantees for targets that are merely log-smooth rather than strongly convex.
New high-dimensional theory for dependent observations turns pointwise sieve estimators into simultaneous inference tools.
· “Simultaneous Inference for Nonlinear Time Series, a Sieve M-regression Approach”
New methods generate random numbers from this distribution at constant speed regardless of shape parameters and support Bayesian models.
· “The Pearson IV distribution: Random variate generation and applications”
A running product of threshold bets keeps type I error capped at every stop while growing exponentially under alternatives.
· “Betting on Bets: Anytime-Valid Tests for Stochastic Dominance”
PToTR constrains the coefficient tensor to a low-rank form so that estimated rates remain positive for tensor responses and tensor inputs.
· “Poisson-response Tensor-on-Tensor Regression and Applications”
The exact threshold is set by the coordinates' fourth moment alone: heavier tails make fitting fail sooner.
Every Bingham parameter matrix gets at least this acceptance probability, so the sampler runs in worst-case polynomial time.
· “A Complexity Bound for the Kent-Ganeiber-Mardia Sampler for the Bingham Distribution”
Even with deployment data in hand, calibration noise sets the floor: relative precision scales as N times the sixth power of s.
· “Physical-Support Confidence Sets for Highly Coherent Dictionaries”
Even with thousands of units, only a few covariates can be balanced; new designs target smaller function classes instead.
· “The Limits of Experimental Design: Covariate Balance Beyond Low Dimension”
Any alarm rule with average run length at least b is a threshold crossing of an e-detector; strong rules also bound every adaptive horizon.
Cox's original exact partial likelihood is asymptotically optimal when tied failure times occur at finitely many instants.
· “Semiparametric efficient estimation of the Cox regression coefficient when there can be ties”
Above that many points, almost surely no centered ellipsoid passes through them all.
· “The sharp SAT/UNSAT phase transition in random ellipsoid fitting”
Cube orientation plus suffix averaging settles agnostic PAC sample complexity up to universal constants.
One coherence condition turns per-intersection e-processes into stopped-FDR and SupFDR guarantees.
An explicit bivariate mixture breaks the conjectured six-mode cap; more peaks than components are real.
· “At least seven modes in a heteroscedastic three-component bivariate Gaussian mixture”
Monotonicity under data processing and additivity on independent products force every such functional to an integral over four strata
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”
A van Trees bound shows each client's samples and privacy budget alone set the limit.
· “A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning”
Covariance decomposition isolates a universal Gaussian term plus explicit fourth-order adjustments for linear statistics of high-dimensional
At any finite sample size, the score 1/p(Y|X) yields the smallest average prediction set among all valid methods.
Optimal edge universality holds even when signal and noise covariance do not commute.
· “Local Laws and Edge Universality for Noncentral Sample Covariance Matrices”
Support reduction makes the NPMLE a finite convex problem; matching impossibility appears at sqrt n noise.
· “Statistical Properties of Nonparametric MLE under Laplace Noise”
A rotation-based test beats classic omnibus tests on single-lag power and spots the 11-year solar cycle without Monte Carlo.
· “Random Invariance Testing on Quadratic Form Statistics with Application to Autocorrelation”
A conditional-sparsity argument yields sharp weighted L^p estimates on every filtered probability space.
· “Weighted Estimation by Discrete-time Sparse Domination on Martingale Spaces”
The limit is integrated Gaussian, so rearranged copula dependence measures are asymptotically normal.
· “Limiting properties of monotone rearrangements of estimators when the truth is flat”
Total import counts survive pooling, but the transport mode behind them is lost—and surveillance pays for it.
Two-stage resampling adds the fourth-order terms, making functional time-series inference formula-free.
Only constant-sum rules make accumulated points a valid skill summary; in nine leagues the uniform rule beats the league's own rule.
A leave-one-out sampler needs O(DTC/ε) parallel steps, bypassing the dimension-scaling barrier of standard τ-leaping.
· “Provably adaptive sampling with uniform and remasking discrete diffusion models”
Singular Bayesian criterion recovers the true number of PCs where BIC undercounts, in theory and simulations.
· “Asymptotics for Model Selection in Probabilistic Principal Component Analysis”
Calibration equations inside the transport program recover the target-to-trial density ratio even with fixed regularization.
A coarse Poincaré inequality, not a manifold, is enough: error is 1/√(n v(h)) for simple eigenvalues.
· “Spectral stability of empirical metric-measure Laplacians”
Under global Clifford shadows, complete U-statistics cut the quadratic degenerate variance from s^2/N to s^2/N^2 relative to batching, and…
· “Batched and Complete U-Statistics for Trace-Polynomial Estimation from Classical Shadows”
For ordered experiment menus, the finite-sample worst-case excess risk F_{n,k_n}(H_n) equals the frontier A_{k_n}{1+o(1)} with no direct…
· “Pre-Disclosure Experiment Menus: Oracle-Relative Risk and Joint Sample--Menu Asymptotics”
In a two-component exponential mixture, informative label missingness can make the full likelihood classifier asymptotically more efficient…
· “Favourable Missingness in Semi-Supervised Classification for Exponential Mixture Models”
Decomposes drug effects into direct, transition, and path-specific pieces without sequential ignorability.
· “Estimating Pathway Treatment Effects in the Presence of Intermediate Events with Multi-State Data”
New guarantee: value estimates stay accurate when either trajectories or horizon length grows, even with thousands of state features.
Analytic p-values replace bootstrap and preserve power at moderate sample sizes.
A finite-sample formula separates target and kernel geometry from their noise levels; smoothness sets the rate.
· “Non-asymptotic Analysis of Mat\'ern Regression: The Roles of Target and Kernel Lengthscales”
Theorem 1: finite-layer voting computes merged contours exactly, no grid inversion needed.
A sorted fit against the noise's quantile profile reaches n^{-1/2} rates under i.i.d. noise.
· “Robust Scale Estimation in Additive Noise via Weighted Order Statistics”
Plug-in regressions misread rewiring as strength change; joint analysis with one rank condition gets the split right.
A one-step corrected estimator keeps Wald and LR tests at nominal size even on the parameter-space boundary.
· “Uniformly Valid Inference Under Interactive and High-Dimensional Constraints”
Two-sided negative-binomial thinning keeps counts integer and beats Poisson and continuous rivals on German infection data.
One scalar function of covariates suffices, for additive, ratio, log, or variance metrics.
It selects predictor groups, prunes within active groups, and keeps interactions subordinate to main effects.
Counting neighbours in equal-area geodesic balls keeps Poisson tests honest on hillsides and bacteria alike.
In a Gaussian-teacher logistic model, the ball's Fisher width divided by √loss settles at an explicit constant.
· “Loss-Parameterized Fisher Width Along Learning Trajectories”
Explicit covariance-adaptive bounds recover the exact FDR under independence and extend to estimated covariances.
· “Further Results on Controlling the False Discovery Rate in Two-Sided Gaussian Mean Testing”
Exact formula: audits through m cannot certify best-of-N reliability; the gap shrinks only with the m²/N scale.
· “The geometry of AI validation: Exact certification limits for iid best-of-N search”
A one-step refinement after recursion locates slope changes to within C sqrt(n log n) at O(n log n) cost.
· “LABS: Extending the scope of binary segmentation via a look-ahead device”
Each tail bound becomes an identity with a named closed-form slack: Gibbs tilt, overshoot, or certificate deficit.
· “Information on trajectories: martingales and random times”
Return-time normalization proves asymptotic normality; for a binary VLMC it holds when m_n log m_n / n → 0.
A logistic-Lasso screen plus refit controls size, hits the minimax detection rate, and runs at p = 22,283.
· “Fast high-dimensional mean testing via logistic regression”
For light-tailed targets, a proposal scale shrinking like d^{−(p−1)/p} keeps worst-case acceptance bounded away from zero.
· “Robustness of random-walk Metropolis for steep potentials”
Under Gaussian sampling, these denominators' noise mirrors their size, so front-door Wald inference survives vanishing mediator noise.
· “Self-Normalizing Denominators in Rational Causal Estimation”
For factorizable copulas from piecewise linear maps, both measures coincide as the product of the factors' taus.
· “Tau-Rho Equality and Other Dependence Measures of a Subclass of Factorizable Copulas”
Modeling zero and near-zero inliers directly beats classical tail estimators on rainfall and insurance data
· “Robust Modeling of Extremes in the Presence of Inliers with Enhanced Tail Estimation”
Two rational one-dimensional models in the probability simplex yield non-algebraic cell boundaries.
· “Boundaries of logarithmic Voronoi cells can be transcendental”
A new descent estimator matches near-optimal rates and points to a computational cliff for planted linear regression.
· “Algorithms for adaptive and heteroskedastic linear regression at the computational threshold”
A new CUSUM variant tunes its 1-bit threshold on the fly and reaches the information-theoretic delay limit.
· “Quickest Change Detection in Parametric Models With 1-Bit Measurements”
Coherence between charge sectors must decay as |Δq|^α with 0 < α ≤ 2 — measurable, not a free choice.
· “The Decoherence Exponent: Stable Phase Noise and Constraints on Objective State Reduction”
Square-free monomial features swap Marchenko-Pastur for a free compound-Poisson law driven by the norm fluctuation.
· “Critical tensor covariance at the Marchenko--Pastur threshold”
New exact distances: 1/3 in a conditioning metric, 1/2^d in the uniform metric, both attained
· “How far are d-dimensional copulas with uniform (d-1)-marginals from (total) independence?”
Regret splits exactly into information loss, scale-change drift, and relative-entropy transport.
· “The concentration game: Bayesian updating, regret, and information”
Momentum-augmented jump processes on hypercubes and lattices recover Hamiltonian speed-ups without embedding the state space.
Covariate terms stay unpenalized, so the intensity splits into interpretable fixed effects plus a smooth RKHS part.
· “An RKHS Framework for Fixed Effects in Permanental Process Models”
Two transforms recover Gamma-Gamma and Lognormal-Rician channel parameters without special-function PDFs.
The paper formalizes a recurring one-person treatment effect that repeated randomized periods can estimate directly.
· “A Primer on Digital Health N-of-1 Studies and Single-Case Designs”
Error bounds computed by resampling compressed rows reach nominal coverage as data and sketch grow.
· “Bootstrap Error Estimation and Sketch-Size Selection for Sketched Ridge Regression”
Drawing radii by stratified quantiles gives smoother log-density coverage than plain IID sampling.
A forward-evolution analysis designs matrix noise schedules and adaptive grids that cut reverse sampling cost.
· “Forward-Evolution Error Analysis and Adaptive Design for Matrix-Valued Diffusion Models”
New proof classifies the bootstrapped top eigenvalue as Weibull, Gaussian, or point mass depending on multipliers.
· “Multiplier Bootstrap and Edge Phase Transitions of High-Dimensional Covariance Matrices”
Independent, non-iid columns with a uniform Poincare inequality suffice for a Wasserstein CLT at rate (log n)^13/sqrt(n).
A theory bounds the bits a session handover needs and the regression error a memory cap costs.
· “Handover of In-Context Learning State Across Session Boundaries”
A new axiom system recovers the exact metric behind perceived complexity, so 'twice as complex' becomes meaningful.
Revealing how graphs 2 through m align leaves a single two-graph problem, making m-graph hardness inherit two-graph thresholds.
· “Converse bounds for multiple graph alignment and correlation detection based on last matching”
One theorem gives two detectors a shared Gaussian limit, even as dimension grows exponentially.
· “Change Point Detection and Localization in High-Dimensional Time Series”
